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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
Article

Summary

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.

Keywords

Stochastic Process Probability Theory Mathematical Biology Initial Configuration Occupation Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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