2003/12/15 by L Turban, L. Turban
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1209/epl/i2003-10165-4
published as Europhys. Lett. 65 (2004) 627-632 · 7 pages, 2 figures
arxiv created 2003/12/15 · arxiv updated 2009/12/01
The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using the method of moments. When the number of iterations goes to infinity, a time-independent asymptotic density is obtained. It has a simple symmetric exponential form which is stable against the modification of a finite number of iterations. When n is large, the deviation from the stationary density is exponentially small in n. The continuum results are compared to Monte Carlo data for the discrete iterated random walk.