# On a random walk with memory and its relation to Markovian processes - Condensed Matter > Statistical Mechanics

On a random walk with memory and its relation to Markovian processes - Condensed Matter > Statistical Mechanics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study a one-dimensional random walk with memory in which the step lengthsto the left and to the right evolve at each step in order to reduce thewandering of the walker. The feedback is quite efficient and lead to anon-diffusive walk. The time evolution of the displacement is given by anequivalent Markovian dynamical process. The probability density for theposition of the walker is the same at any time as for a random walk withshrinking steps, although the two-time correlation functions are quitedifferent.

Author: ** L. Turban Groupe de Physique Statistique, Département P2M, Institut Jean Lamour, Nancy-Université**

Source: https://arxiv.org/