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Toeplitz matrices and random walks with memory

✍ Scribed by Douglas Poland

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
439 KB
Volume
223
Category
Article
ISSN
0378-4371

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✦ Synopsis

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 ofj 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 ofj.

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