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On a Random Graph Related to Quantum Theory

Published online by Cambridge University Press:  01 September 2007

SVANTE JANSON
SVANTE JANSON*
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden (e-mail: [email protected]://www.math.uu.se/~svante/)
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Abstract

We show that a random graph studied by Ioffe and Levit is an example of an inhomogeneous random graph of the type studied by Bollobás, Janson and Riordan, which enables us to give a new, and perhaps more revealing, proof of their result on a phase transition.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 5 , September 2007 , pp. 757 - 766
Copyright
Copyright © Cambridge University Press 2007

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References

[1]Aizenman, M., Klein, A. and Newman, C. M. (1993) Percolation methods for disordered quantum Ising models. In Phase Transitions: Mathematics, Physics, Biology (Kotecky, R., ed.), World Scientific, Singapore, pp. 1–26.Google Scholar
[2]Bollobás, B. (2001) Random Graphs, 2ndedn, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
[3]Bollobás, B., Janson, S. and Riordan, O. The phase transition in inhomogeneous random graphs. Random Struct. Alg., to appear. Available at: arXiv:math.PR/0504589Google Scholar
[4]Ioffe, D. and Levit, A. (2006) Long range order and giant components of quantum random graphs. Preprint. Available at: http://iew3.technion.ac.il/Home/Users/ioffe.htmlGoogle Scholar
[5]Janson, S., Łuczak, T. and Ruciński, A. (2000) Random Graphs, Wiley, New York.CrossRefGoogle Scholar