Location of Repository

Expected Coalescence Time for a Nonuniform Allocation Process

By John K. Mcsweeney and Boris G. Pittel

Abstract

We study a process where balls are repeatedly thrown into n boxes independently according to some probability distribution p. We start with n balls, and at each step all balls landing in the same box are fused into a single ball; the process terminates when there is only one ball left (coalescence). Let c: = P j p2j, the collision probability of two fixed balls. We show that the expected coalescence time is asymptotically 2c −1, under two constraints on p that exclude a thin set of distributions p. One of the constraints is c ≪ ln −2 n. This ln −2 n is shown to be a threshold value: for c ≫ ln −2 n, there exists p with c(p) = c such that the expected coalescence time far exceeds c −1. Connections to coalescent processes in population biology and theoretical computer science are discussed

Topics: Fisher model, random functions, Markov chain, asymptotic behavior
OAI identifier: oai:CiteSeerX.psu:10.1.1.311.2982
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://arxiv.org/pdf/0809.4233... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.