# Detecting the trail of a random walker in random scenery.

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Let G be a transient graph, and flip a fair coin at each vertex.

This gives a distribution P. Now start a random walk from a vertex v, and

retoss the coin at each visited vertex, this time with probability 0.75

for heads and probability 0.25 for tails. The eventual configuration of

the coins gives a distribution Q. Are P and Q absolutely continuous w.r.t.

each other? are they singular? (i.e. can you tell whether a random walker

had tampered with the coins or not?) In the talk I'll answer to this

question for various graphs and various types of random walk. Based on

joint work with Y. Peres.