In this note we establish that the probability that the simple random walk on Z^2 returns to its origin before leaving a strip of width L has asymptotically the same probability as the one for hitting the origin before exiting the centered box of the same size. We also generalize this theorem for fairly arbitrary sequences of increasing sets in Z^2.
|Translated title of the contribution||A note on the simple random walk on Z2: probability of exiting sequences of sets|
|Pages (from-to)||891 - 897|
|Number of pages||7|
|Journal||Statistics and Probability Letters|
|Publication status||Published - May 2006|