Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks
Statistical Mechanics
2007-08-06 v2
Abstract
An analytic formulation of memory-possessing random walks introduced recently [Cressoni et al., Phys. Rev. Lett. 98, 070603 (2007) and Sch\"utz and Trimper, Phys. Rev. E 70, 045101 (2004)] for Alzheimer behavior and related phenomena is provided along with exact solutions on the basis of Fokker-Planck equations. The solution of a delay-differential equation derived for the purpose is shown to produce log-periodic oscillations and to coincide rather accurately with previously published computer simulation results. Generalizations along several directions are also constructed on the basis of the formalism.
Keywords
Cite
@article{arxiv.0708.0034,
title = {Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks},
author = {V. M. Kenkre},
journal= {arXiv preprint arXiv:0708.0034},
year = {2007}
}
Comments
4 pages, 1 fig