Large deviations for independent random walks

J. Theodore Cox, Richard Durrett

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)67-82
Number of pages16
JournalProbability Theory and Related Fields
Issue number1
StatePublished - Mar 1990

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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