Large deviations for independent random walks

J. Theodore Cox; Richard Durrett

doi:10.1007/BF01288559

Large deviations for independent random walks

J. Theodore Cox, Richard Durrett

Department of Mathematics

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

3 Scopus citations

Abstract

We consider a system of independent random walks on ℤ. Let ξ_n(x) be the number of particles at x at time n, and let L_n(x)=ξ₀(x)+ ... +ξ_n(x) be the total occupation time of x by time n. In this paper we study the large deviations of L_n(0)-L_n(1). The behavior we find is much different from that of L_n(0). We investigate the limiting behavior when the initial configurations has asymptotic density 1 and when ξ₀(x) are i.i.d Poisson mean 1, finding that the asymptotics are different in these two cases.

Original language	English (US)
Pages (from-to)	67-82
Number of pages	16
Journal	Probability Theory and Related Fields
Volume	84
Issue number	1
DOIs	https://doi.org/10.1007/BF01288559
State	Published - Mar 1990

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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title = "Large deviations for independent random walks",

abstract = "We consider a system of independent random walks on ℤ. Let ξn(x) be the number of particles at x at time n, and let Ln(x)=ξ0(x)+ ... +ξn(x) be the total occupation time of x by time n. In this paper we study the large deviations of Ln(0)-Ln(1). The behavior we find is much different from that of Ln(0). We investigate the limiting behavior when the initial configurations has asymptotic density 1 and when ξ0(x) are i.i.d Poisson mean 1, finding that the asymptotics are different in these two cases.",

author = "Cox, {J. Theodore} and Richard Durrett",

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AU - Durrett, Richard

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N2 - We consider a system of independent random walks on ℤ. Let ξn(x) be the number of particles at x at time n, and let Ln(x)=ξ0(x)+ ... +ξn(x) be the total occupation time of x by time n. In this paper we study the large deviations of Ln(0)-Ln(1). The behavior we find is much different from that of Ln(0). We investigate the limiting behavior when the initial configurations has asymptotic density 1 and when ξ0(x) are i.i.d Poisson mean 1, finding that the asymptotics are different in these two cases.

AB - We consider a system of independent random walks on ℤ. Let ξn(x) be the number of particles at x at time n, and let Ln(x)=ξ0(x)+ ... +ξn(x) be the total occupation time of x by time n. In this paper we study the large deviations of Ln(0)-Ln(1). The behavior we find is much different from that of Ln(0). We investigate the limiting behavior when the initial configurations has asymptotic density 1 and when ξ0(x) are i.i.d Poisson mean 1, finding that the asymptotics are different in these two cases.

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1

ER -

Large deviations for independent random walks

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