Open Access
2013 Detecting the trail of a random walker in a random scenery
Noam Berger, Yuval Peres
Author Affiliations +
Electron. J. Probab. 18: 1-18 (2013). DOI: 10.1214/EJP.v18-2367


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.<br />


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Noam Berger. Yuval Peres. "Detecting the trail of a random walker in a random scenery." Electron. J. Probab. 18 1 - 18, 2013.


Accepted: 3 October 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1290.60050
MathSciNet: MR3119085
Digital Object Identifier: 10.1214/EJP.v18-2367

Primary: 60G50
Secondary: 60K37

Keywords: branching number , Random scenery , Random walk , Relative entropy

Vol.18 • 2013
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