WIAS Preprint No. 1057, (2005)

Moments and distribution of the local time of a random walk on $Z^2$



Authors

  • Černý, Jiri

2010 Mathematics Subject Classification

  • 60F15 60G50

Keywords

  • random walk, local time

Abstract

Let l(n,x) be the local time of a random walk on Z^2. We prove a strong law of large numbers for the quantity L_n(a)=sum_xin Z^2 l(n,x)^a $ for all a>0. We use this result to describe the distribution of the local time of a typical point in the range of the random walk.

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