Quenched large deviations for multidimensional random walk in random environment with holding times

Details Quenched large deviations for multidimensional random walk in random environment with holding times Quenched large deviations for multidimensional random walk in random environment with holding times

2012-02-25

arxiv.org/abs/1202.5643v1

Mathematics

Probability

21 pages

Scientific paper

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is quenched large deviation principles for the position of the random walk. The rate function is given by the Legendre transform of so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.

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