Math @ Duke

Publications [#243454] of Richard T. Durrett
Papers Published
 Cox, JT; Durrett, R, Large deviations for independent random walks,
Probability Theory and Related Fields, vol. 84 no. 1
(1990),
pp. 6782, ISSN 01788051 [doi]
(last updated on 2018/03/24)
Abstract: We consider a system of independent random walks on ℤ. Let ξn(x) be the number of particles at x at time n, and let Ln(x)=ξ0(x)+ ... +ξn(x) be the total occupation time of x by time n. In this paper we study the large deviations of Ln(0)Ln(1). The behavior we find is much different from that of Ln(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. © 1990 SpringerVerlag.


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