Diffusivity of a random walk on random walks. Issue 2 (16th April 2014) - Boissard, Emmanuel; Cohen, Serge; Espinasse, Thibault; Norris, James
Abstract We consider a random walk <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj23twfzz7" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />(Zn(1), …, Zn(K+1))∈ℤK+1</alternatives> with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj23twg02w" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />σK2=2K+2</alternatives> with respect to the case of the classical simple random walk without constraint. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 267–283, 2015