Distinguishing sceneries by observing the scenery along a random walk path |
| |
Authors: | Itai Benjamini Harry Kesten |
| |
Institution: | (1) Department of Mathematics, Weizmann Institute of Science, 76100 Rehovot, Israel;(2) Department of Mathematics White Hall, Cornell University, 14853 Ithaca, NY, USA |
| |
Abstract: | LetG be an infinite connected graph with vertex setV. Ascenery onG is a map ξ :V → 0, 1 (equivalently, an assignment of zeroes and ones to the vertices ofG). LetS n n≥0 be a simple random walk onG, starting at some distinguished vertex v0. Now let ξ and η be twoknown sceneries and assume that we observe one of the two sequences ξ(S n) n≥0 or {η(S n)} n≥0 but we do not know which of the two sequences is observed. Can we decide, with a zero probability of error, which of the two sequences is observed? We show that ifG = Z orG = Z2, then the answer is “yes” for each fixed ξ and “almost all” η. We also give some examples of graphsG for which almost all pairs (ξ, η) are not distinguishable, and discuss some variants of this problem. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|