Probability Theory and Related Fields

, Volume 84, Issue 1, pp 67–82 | Cite as

Large deviations for independent random walks

  • J. Theodore Cox
  • Richard Durrett


We consider a system of independent random walks on ℤ. Let ξ n (x) be the number of particles atx at timen, and letL n (x)=ξ0(x)+ ... +ξ n (x) be the total occupation time ofx by timen. In this paper we study the large deviations ofL n (0)−L n (1). The behavior we find is much different from that ofL 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.


Stochastic Process Probability Theory Mathematical Biology Initial Configuration Occupation Time 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • J. Theodore Cox
    • 1
  • Richard Durrett
    • 2
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA

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