Moments and distribution of the local time of a random walk on $Z^2$
- Černý, Jiri
2010 Mathematics Subject Classification
- 60F15 60G50
- random walk, local time
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.