Toeplitz matrices and random walks with memory

Douglas Poland

Physica A: Statistical Mechanics and its Applications, 1996, vol. 223, issue 1, 113-124

Abstract: We use a technique based on Toeplitz matrices to calculate the probability distribution for certain random walks on a lattice in continuous time where the walker can take steps of various sizes in each direction and where the probability of a step depends on the nature of a finite set of previous steps. If k(ij) is the rate constant for a step of j units given a history of type i, then we can solve the random walk problem for the special case when the sum over k(ij) is independent of j.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:223:y:1996:i:1:p:113-124

DOI: 10.1016/0378-4371(95)00283-9

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