Subexponential tail asymptotics for a random walk with randomly placed one-way nodes
Maximal displacement for bridges of random walks in a random environment
It is well known that the distribution of simple random walks on ℤ conditioned on returning to the origin after 2 steps does not depend on =(1=1), the probability of moving to the right. Moreover, conditioned on {2=0} the maximal displacement max≤2| | converges in distribution when scaled by √ (diffusive scaling). We consider the analogous problem for transient random walks in random environments on ℤ. We show that under the quenched law (conditioned on the environment...
Asymptotics for the survival probability in a killed branching random walk
Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope − , where denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when → 0, this probability decays like exp{−(+o(1)) / 1/2}, where is a positive constant depending...
The infinite valley for a recurrent random walk in random environment
We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the – suitably centered – empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov, see (1984) 491–506. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time of the RWRE...
Annealed deviations of random walk in random scenery
The voter model with anti-voter bonds
Survival time of random walk in random environment among soft obstacles.
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