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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 sometransition probability after a random holding time. Both the transitionprobabilities and the laws of the holding times are randomly distributed overthe integer lattice. Our main result is a quenched large deviation principlefor the position of the random walk. The rate function is given by the Legendretransform of the so-called Lyapunov exponents for the Laplace transform of thefirst passage time. By using this representation, we derive some asymptotics ofthe rate function in some special cases.

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