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On the Distribution of the Number of Zero Partial Sums

Published online by Cambridge University Press:  14 July 2016

Ora Engelberg Percus  and
Jerome K. Percus
Ora Engelberg Percus
Affiliation:
City College, City University of New York
Jerome K. Percus
Affiliation:
Courant Institute of Mathematical Sciences, New York University
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Abstract

A weighted Markov chain technique is used to determine the general distribution of the number of tie positions in a two candidate ballot. This may be interpreted as the distribution of the number of returns to the origin in an asymmetric random walk, when the particle at each step moves μ units in the positive direction and γ units in the negative direction, given the total number of positive steps and the number of negative steps. Explicit results are obtained when γ = 1, whereas the case of μ and γ ≠ 1 is solved in the form of a generating function.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 162 - 176
Copyright
Copyright © Applied Probability Trust 

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References

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