Exact moments in a continuous time random walk with complete memory of its history

Details Exact moments in a continuous time random walk with complete memory of its history Exact moments in a continuous time random walk with complete memory of its history

2006-03-20

arxiv.org/abs/cond-mat/0603476v2

Phys. Rev. E 74, 032101 (2006)

Physics

Condensed Matter

Statistical Mechanics

Revtex4, 10 pages, 2 figures. v2: applications discussed, clarity improved, corrected scaling of third moment

Scientific paper

10.1103/PhysRevE.74.032101

We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is Poisson distributed. We analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion. These transitions, which are also present in the discrete time case, arise from the memory of the process and are not reproduced by Fokker-Planck approximations to the evolution equation of this random walk.

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