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We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of valleys of height $log t$. In the quenched setting, we also sharply estimate the distribution of the walk at time $t$.
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d ge 3$ and the environment is not too random, then, the total population gro
We consider a nearest-neighbor, one-dimensional random walk ${X_n}_{ngeq 0}$ in a random i.i.d. environment, in the regime where the walk is transient with speed v_P > 0 and there exists an $sin(1,2)$ such that the annealed law of $n^{-1/s} (X_n - n
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the
We give new criteria for ballistic behavior of random walks in random environment which are perturbations of the simple symmetric random walk on $mathbb Z^d$ in dimensions $dge 4$. Our results extend those of Sznitman [Ann. Probab. 31, no. 1, 285-322
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 p