Articles in peer-reviewed journals
| Iterated random walk |
| Turban L. |
| Europhysics Letters 65 (2004) 627 |
| DOI : 10.1209/epl/i2003-10165-4 |
| ArXiv : cond-mat/0312358 [PDF] |
| HAL : hal-00107506 |
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 n â+´ â^z, 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. |