| Título: | Detecting the trail of a random walker in a random scenery |
| Autores: |
Berger, Noam; Hebrew University of Jerusalem and Technical University of Munich Peres, Yuval; Microsoft Research |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Random walk, Random scenery, Relative entropy, Branching number 60G50, 60K37 |
| Descripción: | Suppose that the vertices of the lattice $\mathbb{Z}^d$ are endowed with a random scenery, obtained by tossing a fair coin at each vertex. A random walker, starting from the origin, replaces the coins along its path by i.i.d. biased coins. For which walks and dimensions can the resulting scenery be distinguished from the original scenery? We find the answer for simple random walk, where it does not depend on dimension, and for walks with a nonzero mean, where a transition occurs between dimensions three and four. We also answer this question for other types of graphs and walks, and raise several new questions. |
| Idioma: | Inglés |
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