Abstract
The iterated random walk is a random process in which a randomwalker moves on a one-dimensional random walk which is itselftaking place on a one-dimensional random walk, and so on. Thisprocess is investigated in the continuum limit using the methodof moments. When the number of iterations n → ∞, atime-independent asymptotic density is obtained. It has a simplesymmetric exponential form which is stable against themodification of a finite number of iterations. When n is large,the deviation from the stationary density is exponentially smallin n. The continuum results are compared to Monte Carlo datafor the discrete iterated random walk.
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