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Detecting the trail of a random walker in a random scenery


 
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1. Title Title of document Detecting the trail of a random walker in a random scenery
 
2. Creator Author's name, affiliation, country Noam Berger; Hebrew University of Jerusalem and Technical University of Munich; Israel
 
2. Creator Author's name, affiliation, country Yuval Peres; Microsoft Research; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walk, Random scenery, Relative entropy, Branching number
 
3. Subject Subject classification 60G50, 60K37
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ERC, ISF
 
7. Date (YYYY-MM-DD) 2013-10-03
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2367
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2367
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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