Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T09:52:54.642Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 October 2014

Dan Romik
Affiliation:
University of California, Davis
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Aitken, A. C. 1943. The monomial expansion of determinantal symmetric functions. Proc. Royal Soc. Edinburgh (A), 61, 300–310.Google Scholar
[2] Aldous, D., and Diaconis, P. 1995. Hammersley's interacting particle process and longest increasing subsequences. Probab. Theory Related Fields, 103, 199–213.CrossRefGoogle Scholar
[3] Aldous, D., and Diaconis, P. 1999. Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem. Bull. Amer. Math. Soc., 36, 413–432.CrossRefGoogle Scholar
[4] Anderson, G. W., Guionnet, A., and Zeitouni, O. 2010. An Introduction to Random Matrices. Cambridge University Press.Google Scholar
[5] Andrews, G. E., Askey, R., and Roy, R. 2001. Special Functions. Cambridge University Press.Google Scholar
[6] Angel, O., Holroyd, A. E., Romik, D., and Virág, B. 2007. Random sorting networks. Adv. Math., 215, 839–868.CrossRefGoogle Scholar
[7] Angel, O., Holroyd, A. E., and Romik, D. 2009. The oriented swap process. Ann. Probab., 37, 1970–1998.CrossRefGoogle Scholar
[8] Apostol, T. M. 1990. Modular Forms and Dirichlet Series in Number Theory. 2nd edition. Springer.CrossRefGoogle Scholar
[9] Arnold, V. I. 1988. Mathematical Methods of Classical Mechanics. 2nd edition. Springer.Google Scholar
[10] Baer, R. M., and Brock, P. 1968. Natural sorting over permutation spaces. Math. Comp., 22, 385–410.CrossRefGoogle Scholar
[11] Baik, J., Deift, P., and Johansson, K. 1999a. On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc., 12, 1119–1178.CrossRefGoogle Scholar
[12] Baik, J., Deift, P., and Johansson, K. 1999b. On the distribution of the length of the second row of a Young diagram under Plancherel measure. Geom. Funct. Anal, 10, 702–731.Google Scholar
[13] Balázs, M., Cator, E., and Seppäläinen, T. 2006. Cube root fluctuations for the corner growth model associated to the exclusion process. Electron. J. Probab., 11, 1094–1132.CrossRefGoogle Scholar
[14] Bivins, R. L., Metropolis, N., Stein, P. R., and Wells, M. B. 1954. Characters of the symmetric groups of degree 15 and 16. Math. Comp., 8, 212–216.CrossRefGoogle Scholar
[15] Blair-Stahn, N. First passage percolation and competition models. Preprint, arXiv:1005.0649, 2010.
[16] Bollobás, B., and Brightwell, G. 1992. The height of a random partial order: concentration of measure. Ann. Appl. Probab., 2, 1009–1018.CrossRefGoogle Scholar
[17] Bollobás, B., and Winkler, P. 1988. The longest chain among random points in Euclidean space. Proc. Amer. Math. Soc., 103, 347–353.CrossRefGoogle Scholar
[18] Bornemann, F. 2010. On the numerical evaluation of distributions in random matrix theory: A review. Markov Process. Related Fields, 16, 803–866.Google Scholar
[19] Borodin, A., Okounkov, A., and Olshanski, G. 2000. Asymptotics of Plancherel measures for symmetric groups. J. Amer. Math. Soc., 13, 491–515.CrossRefGoogle Scholar
[20] Boucheron, S., Lugosi, G., and Bousquet, O. 2004. Concentration inequalities. Pages 208–240 of: Bousquet, O., von Luxburg, U., and Rätsch, G. (eds), Advanced Lectures in Machine Learning. Springer.Google Scholar
[21] Bressoud, D. 1999. Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture. Cambridge University Press.CrossRefGoogle Scholar
[22] Brown, J. W., and Churchill, R. 2006. Fourier Series and Boundary Value Problems. 7th edition. McGraw-Hill.Google Scholar
[23] Bufetov, A. I. 2012. On the Vershik-Kerov conjecture concerning the Shannon-McMillan-Breiman theorem for the Plancherel family of measures on the space of Young diagrams. Geom. Funct. Anal., 22, 938–975.CrossRefGoogle Scholar
[24] Ceccherini-Silberstein, T., Scarabotti, F., and Tolli, F. 2010. Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras. Cambridge University Press.CrossRefGoogle Scholar
[25] Chowla, S., Herstein, I. N., and Moore, W. K. 1951. On recursions connected with symmetric groups I. Canad. J. Math., 3, 328–334.CrossRefGoogle Scholar
[26] Clarkson, P. A., and McLeod, J. B. 1988. A connection formula for the second Painlevé transcendent. Arch. Rat. Mech. Anal., 103, 97–138.CrossRefGoogle Scholar
[27] Cohn, H., Elkies, N., and Propp, J. 1996. Local statistics for random domino tilings of the Aztec diamond. Duke Math. J., 85, 117–166.Google Scholar
[28] Cohn, H., Larsen, M., and Propp, J. 1998. The shape of a typical boxed plane partition. New York J. Math., 4, 137–165.Google Scholar
[29] Daley, D. J., and Vere-Jones, D. 2003. An Introduction to the Theory of Point Processes, Vol. I: Elementary Theory and Methods. 2nd edition. Springer.Google Scholar
[30] Deift, P. 2000. Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach. American Mathematical Society.Google Scholar
[31] Dembo, A., and Zeitouni, O. 1998. Large Deviations Techniques and Applications. 2nd edition. Springer.CrossRefGoogle Scholar
[32] Deuschel, J.-D., and Zeitouni, O. 1999. On increasing subsequences of I.I.D. samples. Combin. Probab. Comput., 8, 247–263.CrossRefGoogle Scholar
[33] Durrett, R. 2010. Probability: Theory and Examples. 4th edition. Cambridge University Press.CrossRefGoogle Scholar
[34] Edelman, P., and Greene, C. 1987. Balanced tableaux. Adv. Math., 63, 42–99.CrossRefGoogle Scholar
[35] Edwards, H. M. 2001. Riemann's Zeta Function. Dover.Google Scholar
[36] Efron, B., and Stein, C. 1981. The jackknife estimate of variance. Ann. Stat., 9, 586–596.CrossRefGoogle Scholar
[37] Elkies, N., Kuperberg, G., Larsen, M., and Propp, J. 1992. Alternating sign matrices and domino tilings. J. Algebraic Combin., 1, 111–132; 219–234.Google Scholar
[38] Estrada, R., and Kanwal, R. P. 2000. Singular Integral Equations. Birkhäuser.CrossRefGoogle Scholar
[39] Feit, W. 1953. The degree formula for the skew-representations of the symmetric group. Proc. Amer. Math. Soc., 4, 740–744.CrossRefGoogle Scholar
[40] Feller, W. 1967. A direct proof of Stirling's formula. Amer. Math. Monthly, 74, 1223–1225.CrossRefGoogle Scholar
[41] Feller, W. 1968. An Introduction to Probability Theory and its Applications, Vol. 1. 3rd edition. Wiley.Google Scholar
[42] Forrester, P. J. 2010. Log-Gases and Random Matrices. Princeton University Press.Google Scholar
[43] Frame, J. S., Robinson, G. de B., and Thrall, R. M. 1954. The hook graphs of the symmetric group. Canad. J. Math., 6, 316–324.CrossRefGoogle Scholar
[44] Franzblau, D. S., and Zeilberger, D. 1982. A bijective proof of the hook-length formula. J. Algorithms, 3, 317–343.CrossRefGoogle Scholar
[45] Frieze, A. 1991. On the length of the longest monotone subsequence in a random permutation. Ann. Appl. Probab., 1, 301–305.CrossRefGoogle Scholar
[46] Fristedt, B. 1993. The structure of random partitions of large integers. Trans. Amer. Math. Soc., 337, 703–735.CrossRefGoogle Scholar
[47] Gessel, I. M. 1990. Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A, 53, 257–285.CrossRefGoogle Scholar
[48] Goodman, N. R. 1963. Statistical analysis based on a certain multivariate complex gaussian distribution (an introduction). Ann. Math. Statist., 34, 152–177.CrossRefGoogle Scholar
[49] Graham, R. L., Knuth, D. E., and Patashnik, O. 1994. Concrete Mathematics. Addison-Wesley.Google Scholar
[50] Greene, C., Nijenhuis, A, and Wilf, H. S. 1979. A probabilistic proof of a formula for the number of Young tableaux of a given shape. Adv. Math., 31, 104–109.CrossRefGoogle Scholar
[51] Greene, C., Nijenhuis, A, and Wilf, H. S. 1984. Another probabilistic method in the theory of Young tableaux. J. Comb. Theory Ser. A, 37, 127–135.CrossRefGoogle Scholar
[52] Groeneboom, P. 2002. Hydrodynamical methods for analyzing longest increasing subsequences. J. Comp. Appl. Math., 142, 83–105.CrossRefGoogle Scholar
[53] Haiman, M. D. 1989. On mixed insertion, symmetry, and shifted Young tableaux. J. Comb. Theory Ser. A, 50, 196–225.CrossRefGoogle Scholar
[54] Hammersley, J.M. 1972. A few seedlings of research. Pages 345–394 of: LeCam, L. M., Neyman, J., and Scott, E. L. (eds), Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Theory of Statistics. University of California Press.Google Scholar
[55] Hamming, R. W. 1980. The unreasonable effectiveness of mathematics. Amer. Math. Monthly, 87, 81–90.CrossRefGoogle Scholar
[56] Hardy, G. H., and Ramanujan, S. 1918. Asymptotic formulae in combinatory analysis. Proc. London Math. Soc., s2-17, 75–115.CrossRefGoogle Scholar
[57] Hastings, S. P., and McLeod, J. B. 1980. A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal., 73, 35–51.CrossRefGoogle Scholar
[58] Hiai, F., and Petz, D. 2000. The Semicircle Law, Free Random Variables and Entropy. American Mathematical Society.Google Scholar
[59] Hough, J. B., Krishnapur, M., Peres, Y., and Virág, B. 2009. Zeros of Gaussian Analytic Functions and Determinantal Point Processes. American Mathematical Society.CrossRefGoogle Scholar
[60] Jockusch, W., Propp, J., and Shor, P. Domino tilings and the arctic circle theorem. Preprint, arXiv:math/9801068, 1998.
[61] Johansson, K. 1998. The longest increasing subsequence in a random permutation and a unitary random matrix model. Math. Res. Letters, 5, 63–82.CrossRefGoogle Scholar
[62] Johansson, K. 2000. Shape fluctuations and random matrices. Commun. Math. Phys., 209, 437–476.CrossRefGoogle Scholar
[63] Johansson, K. 2001. Discrete orthogonal polynomial ensembles and the Plancherel measure. Ann. Math., 153, 259–296.CrossRefGoogle Scholar
[64] Johansson, K. 2002. Non-intersecting paths, random tilings and random matrices. Probab. Theory Related Fields, 123, 225–280.CrossRefGoogle Scholar
[65] Johnstone, I. M. 2001. On the distribution of the largest eigenvalue in principal components analysis. Ann. Stat., 29, 295–327.Google Scholar
[66] Kerov, S. 1998. A differential model of growth of Young diagrams. Pages 111–130 of: Ladyzhenskaya, O. A. (ed), Proceedings of the St Petersburg Mathematical Society Volume IV. American Mathematical Society.Google Scholar
[67] Kim, J. H. 1996. On increasing subsequences of random permutations. J. Comb. Theory Ser. A, 76, 148–155.CrossRefGoogle Scholar
[68] King, F. W. 2009. Hilbert Transforms, Vols. 1–2. Cambridge University Press.Google Scholar
[69] Kingman, J. F. C. 1968. The ergodic theory of subadditive processes. J. Roy. Stat. Soc. B, 30, 499–510.Google Scholar
[70] Knuth, D. E. 1970. Permutations, matrices, and generalized Young tableaux. Pacific J. Math., 34, 316–380.CrossRefGoogle Scholar
[71] Knuth, D. E. 1998. The Art of Computer Programming, Vol. 3: Sorting and Searching. 2nd edition. Addison-Wesley.Google Scholar
[72] König, W. 2005. Orthogonal polynomial ensembles in probability theory. Probab. Surv., 2, 385–447.CrossRefGoogle Scholar
[73] Korenev, B. G. 2002. Bessel Functions and Their Applications. CRC Press.Google Scholar
[74] Lax, P. D. 2002. Functional Analysis. Wiley-Interscience.Google Scholar
[75] Lifschitz, V., and Pittel, B. 1981. The number of increasing subsequences of the random permutation. J. Comb. Theory Ser. A, 31, 1–20.CrossRefGoogle Scholar
[76] Liggett, T. M. 1985a. An improved subadditive ergodic theorem. Ann. Probab., 13, 1279–1285.CrossRefGoogle Scholar
[77] Liggett, T. M. 1985b. Interacting Particle Systems. Springer.CrossRefGoogle Scholar
[78] Liggett, T. M. 1999. Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer.CrossRefGoogle Scholar
[79] Logan, B. F., and Shepp, L. A. 1977. A variational problem for random Young tableaux. Adv. Math., 26, 206–222.CrossRefGoogle Scholar
[80] Lyons, R. 2003. Determinantal probability measures. Publ. Math. Inst. Hautes Études Sci., 98, 167–212.CrossRefGoogle Scholar
[81] Lyons, R. 2014. Determinantal probability: basic properties and conjectures. To appear in Proc. International Congress of Mathematicians, Seoul, Korea.Google Scholar
[82] Lyons, R., and Steif, J. E. 2003. Stationary determinantal processes: phase multiplicity, Bernoullicity, entropy, and domination. Duke Math. J., 120, 515–575.Google Scholar
[83] Macchi, O. 1975. The coincidence approach to stochastic point processes. Adv. Appl. Prob., 7, 83–122.CrossRefGoogle Scholar
[84] Mallows, C. L. 1963. Problem 62-2, patience sorting. SIAM Rev., 5, 375–376.CrossRefGoogle Scholar
[85] Mallows, C. L. 1973. Patience sorting. Bull. Inst. Math. Appl., 9, 216–224.Google Scholar
[86] Martin, J. 2006. Last-passage percolation with general weight distribution. Markov Process. Related Fields, 273–299.Google Scholar
[87] McKay, J. 1976. The largest degrees of irreducible characters of the symmetric group. Math. Comp., 30, 624–631.CrossRefGoogle Scholar
[88] Mehta, M. L. 2004. Random Matrices. 3rd edition. Academic Press.Google Scholar
[89] Miller, K. S., and Ross, B. 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley-Interscience.Google Scholar
[90] Mountford, T., and Guiol, H. 2005. The motion of a second class particle for the tasep starting from a decreasing shock profile. Ann. Appl. Probab., 15, 1227–1259.CrossRefGoogle Scholar
[91] Newman, D. J. 1997. Analytic number theory. Springer.Google Scholar
[92] Novelli, J.-C., Pak, I., and Stoyanovskii, A. V. 1997. A direct bijective proof of the hook-length formula. Discr. Math. Theor. Comp. Sci., 1, 53–67.Google Scholar
[93] Odlyzko, A. M. 1995. Asymptotic enumeration methods. Pages 1063–1229 of: Graham, R. L., Groetschel, M., and Lovász, L. (eds), Handbook of Combinatorics, Vol. 2. Elsevier.Google Scholar
[94] Odlyzko, A. M., and Rains, E. M. 2000. On longest increasing subsequences in random permutations. Pages 439–451 of: Grinberg, E. L., Berhanu, S., Knopp, M., Mendoza, G., and Quinto, E. T. (eds), Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis. American Mathematical Society.Google Scholar
[95] Okounkov, A. 2000. Random matrices and random permutations. Int. Math. Res. Notices, 2000, 1043–1095.CrossRefGoogle Scholar
[96] Pak, I. 2001. Hook length formula and geometric combinatorics. Sém. Lothar. Combin., 46, Article B46f.Google Scholar
[97] Peché, S. 2009. Universality results for the largest eigenvalues of some sample covariance matrix ensembles. Probab. Theory Related Fields, 143, 481–516.CrossRefGoogle Scholar
[98] Petersen, T. K., and Speyer, D. 2005. An arctic circle theorem for Groves. J. Combin. Theory Ser. A, 111, 137–164.CrossRefGoogle Scholar
[99] Pillai, N., and Yin, J. Universality of covariance matrices. Preprint, arXiv:1110.2501, 2011.
[100] Pittel, B., and Romik, D. Limit shapes for random square Young tableaux and plane partitions. Preprint, arXiv:math/0405190v1, 2004.
[101] Pittel, B., and Romik, D. 2007. Limit shapes for random square Young tableaux. Adv. Appl. Math, 38, 164–209.CrossRefGoogle Scholar
[102] Prähofer, M., and Spohn, H. 2004. Exact scaling functions for one-dimensional stationary KPZ growth. J. Stat. Phys., 115, 255–279. Numerical tables available at http://www-m5.ma.tum.de/KPZ.CrossRefGoogle Scholar
[103] Reiner, V. 2005. Note on the expected number of Yang-Baxter moves applicable to reduced decompositions. Eur. J. Combin., 26, 1019–1021.CrossRefGoogle Scholar
[104] Robinson, G. de B. 1938. On the representations of the symmetric group. Amer. J. Math., 60, 745–760.Google Scholar
[105] Rockafellar, R. T. 1996. Convex Analysis. Princeton University Press.Google Scholar
[106] Romik, D. 2000. Stirling's approximation for n!: the ultimate short proof?Amer. Math. Monthly, 107, 556–557.CrossRefGoogle Scholar
[107] Romik, D. 2005. The number of steps in the Robinson-Schensted algorithm. Funct. Anal. Appl., 39, 152–155.CrossRefGoogle Scholar
[108] Romik, D. 2006. Permutations with short monotone subsequences. Adv. Appl. Math., 37, 501–510.CrossRefGoogle Scholar
[109] Romik, D. 2012. Arctic circles, domino tilings and square Young tableaux. Ann. Probab., 40, 611–647.CrossRefGoogle Scholar
[110] Rost, H. 1981. Nonequilibrium behaviour of a many particle process: density profile and local equilibria. Z. Wahrsch. Verw. Gebiete, 58, 41–53.CrossRefGoogle Scholar
[111] Rudin, W. 1986. Real and Complex Analysis. 3rd edition. McGraw-Hill.Google Scholar
[112] Sagan, B. E. 2001. The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. Springer.CrossRefGoogle Scholar
[113] Schensted, C. 1961. Longest increasing and decreasing subsequences. Canad. J. Math., 13, 179–191.CrossRefGoogle Scholar
[114] Schützenberger, M.-P. 1963. Quelques remarques sur une construction de Schensted. Math. Scand., 12, 117–128.CrossRefGoogle Scholar
[115] Seppäläinen, T. Lecture notes on the corner growth model. Unpublished notes (2009), available at http://www.math.wisc.edu/~seppalai/cornergrowth-book/ajo.pdf.
[116] Seppäläinen, T. 1996. A microscopic model for the Burgers equation and longest increasing subsequences. Electron. J. Probab., 1-5, 1–51.Google Scholar
[117] Seppäläinen, T. 1998a. Hydrodynamic scaling, convex duality and asymptotic shapes of growth models. Markov Process. Related Fields, 4, 1–26.Google Scholar
[118] Seppäläinen, T. 1998b. Large deviations for increasing sequences on the plane. Probab. Theory Related Fields, 112, 221–244.Google Scholar
[119] Simon, B. 1977. Notes on infinite determinants of Hilbert space operators. Adv. Math., 24, 244–273.Google Scholar
[120] Simon, B. 2005. Trace Ideals and Their Applications. 2nd edition. American Mathematical Society.Google Scholar
[121] Soshnikov, A. 2000. Determinantal random point fields. Russian Math. Surveys, 55, 923–975.CrossRefGoogle Scholar
[122] Soshnikov, A. 2002. A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices. J. Stat. Phys., 108, 1033–1056.CrossRefGoogle Scholar
[123] Spitzer, F. 1970. Interaction of Markov processes. Adv. Math., 5, 246–290.CrossRefGoogle Scholar
[124] Stanley, R. P. 1984. On the number of reduced decompositions of elements of Coxeter groups. Eur. J. Combin., 5, 359–372.CrossRefGoogle Scholar
[125] Stanley, R. P. 1999. Enumerative Combinatorics, Vol. 2. Cambridge University Press.CrossRefGoogle Scholar
[126] Stanley, R. P. 2007. Increasing and decreasing subsequences and their variants. Pages 545–579 of: Sanz-Solé, M., Soria, J., Varona, J. L., and Verdera, J. (eds), Proceedings of the International Congress of Mathematicians, Madrid 2006. American Mathematical Society.
[127] Stanley, R. P. 2011. Enumerative Combinatorics, Vol. 1. 2nd edition. Cambridge University Press.CrossRefGoogle Scholar
[128] Steele, J. M. 1986. An Efron-Stein inequality for nonsymmetric statistics. Ann. Stat., 14, 753–758.Google Scholar
[129] Steele, J. M. 1995. Variations on the monotone subsequence theme of Erdős and Szekeres. Pages 111–131 of: Aldous, D., Diaconis, P., Spencer, J., and Steele, J. M. (eds), Discrete Probability and Algorithms. Springer.Google Scholar
[130] Szalay, M., and Turán, P. 1977. On some problems of statistical theory of partitions. I. Acta Math. Acad. Sci. Hungr., 29, 361–379.Google Scholar
[131] Szegő, G. 1975. Orthogonal Polynomials. 4th edition. American Mathematical Society.Google Scholar
[132] Talagrand, M. 1995. Concentration of measure and isoperimetric inequalities in product spaces. Publ. Math. Inst. Hautes Etud. Sci., 81, 73–205.Google Scholar
[133] Temperley, H. 1952. Statistical mechanics and the partition of numbers. The form of the crystal surfaces. Proc. Camb. Philos. Soc., 48, 683–697.CrossRefGoogle Scholar
[134] Thrall, R. M. 1952. A combinatorial problem. Michigan Math. J., 1, 81–88.Google Scholar
[135] Titschmarsh, E. C. 1948. Introduction to the Theory of Fourier Integrals. 2nd edition. Clarendon Press.Google Scholar
[136] Tracy, C. A., and Widom, H. 1994. Level-spacing distributions and the Airy kernel. Commun. Math. Phys., 159, 151–174.CrossRefGoogle Scholar
[137] Tracy, C. A., and Widom, H. 2009. Asymptotics in ASEP with step initial condition. Commun. Math. Physics, 290, 129–154.CrossRefGoogle Scholar
[138] Ulam, S. 1961. Monte Carlo calculations in problems of mathematical physics. Pages 261–281 of: Beckenbach, E. F. (ed), Modern Mathematics For the Engineer, Second Series. McGraw-Hill.Google Scholar
[139] Varadhan, S. R. S. 2008. Large deviations. Ann. Probab., 36, 397–419.CrossRefGoogle Scholar
[140] Vershik, A., and Pavlov, D. 2009. Numerical experiments in problems of asymptotic representation theory. Zap. Nauchn. Sem., 373, 77–93. Translated in J. Math. Sci., 168:351–361, 2010.Google Scholar
[141] Vershik, A. M. 1996. Statistical mechanics of combinatorial partitions and their limit shapes. Funct. Anal. Appl., 30, 90–105.CrossRefGoogle Scholar
[142] Vershik, A. M., and Kerov, S. V. 1977. Asymptotics of the Plancherel measure of the symmetric group and the limiting shape of Young tableaux. Soviet Math. Dokl., 18, 527–531.Google Scholar
[143] Vershik, A. M., and Kerov, S. V. 1985. The asymptotics of maximal and typical dimensions irreducible representations of the symmetric group. Funct. Anal. Appl., 19, 21–31.CrossRefGoogle Scholar
[144] Wang, K. 2012. Random covariance matrices: universality of local statistics of eigenvalues up to the edge. Random Matrices: Theory Appl., 1, 1150005.CrossRefGoogle Scholar
[145] Watson, G. N. 1995. A Treatise on the Theory of Bessel Functions. 2nd edition. Cambridge University Press.Google Scholar
[146] Wigner, E. 1960. The unreasonable effectiveness of mathematics in the natural sciences. Comm. Pure Appl. Math., 13, 1–14.Google Scholar
[147] Wishart, J. 1928. The generalised product moment distribution in samples from a normal multivariate population. Biometrika, 20A, 32–53.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Dan Romik, University of California, Davis
  • Book: The Surprising Mathematics of Longest Increasing Subsequences
  • Online publication: 05 October 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139872003.010
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Dan Romik, University of California, Davis
  • Book: The Surprising Mathematics of Longest Increasing Subsequences
  • Online publication: 05 October 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139872003.010
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Dan Romik, University of California, Davis
  • Book: The Surprising Mathematics of Longest Increasing Subsequences
  • Online publication: 05 October 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139872003.010
Available formats
×