Random walk attracted by percolation clusters.
Detecting a local perturbation in a continuous scenery.
Survival time of random walk in random environment among soft obstacles.
Phase transition for the frog model.
A note on quenched moderate deviations for Sinai’s random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai’s regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is .
Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards
We consider a random walk in a stationary ergodic environment in , with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right which implies that there are no “traps.” We prove the law of large numbers with positive speed, as well as the ergodicity of the environment seen from the particle. Then, we consider Knudsen stochastic billiard with a drift in a random tube in , , which serves as environment....
Soft local times and decoupling of random interlacements
In this paper we establish a decoupling feature of the random interlacement process at level , . Roughly speaking, we show that observations of restricted to two disjoint subsets and of are approximately independent, once we add a sprinkling to the process by slightly increasing the parameter . Our results differ from previous ones in that we allow the mutual distance between the sets and to be much smaller than their diameters. We then provide an important application of this...
A note on quenched moderate deviations for Sinai's random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is exp{-Const ⋅ ln(1))}.
A note on spider walks
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.
A note on spider walks
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.
Macroscopic non-uniqueness and transversal fluctuation in optimal random sequence alignment
We investigate the optimal alignment of two independent random sequences of length . We provide a polynomial lower bound for the probability of the optimal alignment to be macroscopically non-unique. We furthermore establish a connection between the transversal fluctuation and macroscopic non-uniqueness.
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