Large deviations for independent random walks
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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.
KeywordsStochastic Process Probability Theory Mathematical Biology Initial Configuration Occupation Time
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