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Large deviations for independent random walks
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  • Published: March 1990

Large deviations for independent random walks

  • J. Theodore Cox1 &
  • Richard Durrett2 

Probability Theory and Related Fields volume 84, pages 67–82 (1990)Cite this article

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  • 5 Citations

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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.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Syracuse University, 13210, Syracuse, NY, USA

    J. Theodore Cox

  2. Department of Mathematics, Cornell University, White Hall, 14853, Ithaca, NY, USA

    Richard Durrett

Authors
  1. J. Theodore Cox
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  2. Richard Durrett
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Additional information

This work was done while the first author was on sabbatical at Cornell University. Both authors were partially supported by the National Science Foundation and the Army Research Office through the Mathematical Sciences Institute at Cornell

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Cite this article

Cox, J.T., Durrett, R. Large deviations for independent random walks. Probab. Th. Rel. Fields 84, 67–82 (1990). https://doi.org/10.1007/BF01288559

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  • Received: 24 August 1988

  • Revised: 25 April 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01288559

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Initial Configuration
  • Occupation Time
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