We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We study the probability that the random walk travels slower than its typical speed and determine its decay rate asymptotic.
"Slowdown estimates for one-dimensional random walks in random environment with holding times." Electron. Commun. Probab. 23 1 - 12, 2018. https://doi.org/10.1214/18-ECP191