Matrix method for random walks on lattices

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then calculate averages over a given ensemble of paths for both additive and multiplicative properties in a nonstochastic and noniterative fashion. In particular, we can calculate the mean first-passage time between arbitrary groups of stationary points for discrete path sampling databases, and hence extract phenomenological rate constants. We present a number of examples to demonstrate the efficiency and robustness of this approach.

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Graph transformation method for calculating waiting times in Markov chains

Trygubenko

Wales

2006

The Journal of Chemical Physics

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Matrix method for random walks on lattices

Cited by 1 publication

References 7 publications

Graph transformation method for calculating waiting times in Markov chains

Graph transformation method for calculating waiting times in Markov chains

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