IJPAM: Volume 99, No. 3 (2015)

THE DENSITY OF THE PROCESS OF
COLAESCING RANDOM WALKS

Samir Brahim Belhaouari
Department of Mathematics
Alfaisal University
P.O. Box 50927, Riyadh, 11533, SAUDI ARABIA


Abstract. We study the density of the process of coalescing random walks starting from $\Z$ at time 0, where the random walk kernel associated to this model has finite second moment. It is shown that the density equals the survival probability of voter model with the initial condition being all 0's except for a single 1 at the origin and it converges to $\frac{1}{\sqrt{t}}$.

Received: November 10, 2014

AMS Subject Classification: 60G05, 60G40, 60A10

Key Words and Phrases: random walk, coalescing random walks, Voter model

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DOI: 10.12732/ijpam.v99i3.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 3
Pages: 325 - 341


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).