Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks

Details Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks

2007-07-31

arxiv.org/abs/0708.0034v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 fig

Scientific paper

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.

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