The density of the process of colaescing random walks

Samir Brahim Belhaouari

doi:10.12732/ijpam.v99i3.8

The density of the process of colaescing random walks

Samir Brahim Belhaouari^*

^*Corresponding author for this work

Alfaisal University

Research output: Contribution to journal › Article › peer-review

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 1/√t.

Original language	English
Pages (from-to)	325-341
Number of pages	17
Journal	International Journal of Pure and Applied Mathematics
Volume	99
Issue number	3
DOIs	https://doi.org/10.12732/ijpam.v99i3.8
Publication status	Published - 2015
Externally published	Yes

Keywords

Coalescing random walks
Random walk
Voter model

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10.12732/ijpam.v99i3.8

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title = "The density of the process of colaescing random walks",

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 1/√t.",

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AB - 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 1/√t.

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KW - Random walk

KW - Voter model

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DO - 10.12732/ijpam.v99i3.8

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JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

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The density of the process of colaescing random walks

Abstract

Keywords

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