2007/08/28 by Gilch, Lorenz
#20E22 #60B15 (Secondary) #60G50 (Primary) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.0708.3767
Suppose we are given an infinite, finitely generated group G and a transient random walk on the wreath product (ℤ/ 2ℤ)\wr G, such that its projection on G is transient and has finite first moment. This random walk can be interpreted as a lamplighter random walk on G. Our aim is to show that the random walk on the wreath product escapes to infinity with respect to a suitable (pseudo-)metric faster than its projection onto G. We also address the case where the pseudo-metric is the length of a shortest ``travelling salesman tour''. In this context, and excluding some degenerate cases if G=ℤ, the linear rate of escape is strictly bigger than the rate of escape of the lamplighter random walk's projection on G.