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Local Limit Theorems for Random Walks in a 1D Random Environment
RWRE quenched random environments
2015/9/29
We consider random walks (RW) in a one-dimensional i.i.d.
random environment with jumps to the nearest neighbours. For almost
all environments, we prove a quenched Local Limit Theorem (LLT) for
the...
QUENCHED LIMIT THEOREMS FOR NEAREST NEIGHBOUR RANDOM WALKS IN 1D RANDOM ENVIRONMENT
NEIGHBOUR RANDOM WALKS IMIT THEOREMS
2015/9/29
It is well known that random walks in one dimensional random environment can exhibit subdiffusive behavior due
to presence of traps. In this paper we show that the passage times
of diffe...
Branching diffusions in random environment
Branching process random environment diffusion approximation Laplace transform survival probability backbone construction
2011/9/6
Abstract: We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obta...
Annealed and quenched fluctuations for ballistic random walks in random environment on Z
Random walk in random environment stable laws
2011/1/19
We consider transient random walks in random environment on Z in the positive speed
(ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer proves that the hitti...
We survey recent results and open questions on the ballistic phase of stretched polymers in both annealed and quenched random environments
Quenched Lyapunov exponent for the parabolic Anderson model in a dynamic random environment
Quenched Lyapunov exponent parabolic Anderson model
2010/11/9
We continue our study of the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \gamma\xi u$ for the space-time field $u\colon\,\Z^d\times [0,\infty)\to\R$, where $\kappa \in [0,\in...
Convergence in $L^p$ and its exponential rate for a branching process in a random environment
branching process random environment
2010/11/9
We consider a supercritical branching process $(Z_n)$ in a random environment $\xi$. Let $W$ be the limit of the normalized population size $W_n=Z_n/E[Z_n|\xi]$. We first show a necessary and sufficie...
Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards
cosine law stochastic billiard Knudsen random wal random medium random walk in random environment unbounded
2010/11/26
We consider a random walk in a stationary ergodic environment
in Z, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of s...