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.
References
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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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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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DOI: https://doi.org/10.1007/BF01288559
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Initial Configuration
- Occupation Time