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Random Walk Attracted by Percolation Clusters
subcritical percolation subdiffusivity reversibility spectral gap
2009/4/27
Starting with a percolation model in Zd in the subcritical regime, we consider a random walk described as follows: the probability of transition from x to y is proportional to some function f of the s...
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
Random walk random environment zero-one law law of large numbers
2009/4/24
We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, w...
The scaling limit of senile reinforced random walk
senile reinforced random walk scaling limit
2009/4/22
This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable cond...
Uniqueness of the mixing measure for a random walk in a random environment on the positive integers
random walk random environment
2009/4/22
Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An applic...
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
Zero-One Law Random Walk Mixing Random Environment
2009/4/7
We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, w...
Central Limit Theorem For The Excited Random Walk In Dimension d≥2
central limit theorem random walk law
2009/3/30
We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d≥2
Central Limit Theorem For The Excited Random Walk In Dimension d≥2
Central Limit Theorem Random Walk Dimension
2009/3/23
We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d≥2
A functional limit theorem for a 2d-random walk with dependent marginals
functional limit theorem random walk
2009/3/20
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal ...
Random walk on a discrete torus and random interlacements
Random walk discrete torus random interlacements
2009/3/19
We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ)d, d ≥ 3, until u Nd time steps, u > 0, and the model of random interlacements r...
A relation between dimension of the harmonic measure，entropy and drift for a random walk on a hyperbolic space
harmonic measure entropy drift hyperbolic space
2009/3/19
We establish in this paper an exact formula which links the dimension of the harmonic measure, the asymptotic entropy and the rate of escape for a random walk on a discrete subgroup of the isometry gr...