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In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time se...
Given a Harris chain (M,,)n40 on any state space (9C,) with essentially unique stationary measure <, let (Xn)nZObe a sequence of real-valued random variables which are conditionally independent, gi...
In the present paper we consider a continuous time random walk on an anisotropic random lattice. We show the existence of a steady state 0, for the environment process (( (t)),ao corresponding to t...
In this paper, we consider some distributions of maxima of excursions and related variables for standard random walk and Brownian motion. We discuss the infinite divisibility properties of these di...
The Brownian excursion measure is a conformally invariant innite measure on curves. It gured prominently in one of rst major applications of SLE, namely the explicit calculations of the planar Brownia...
Random Walk in Dynamic Markovian Random Environment.
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...
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...
We consider a random walk $S_n = sum_{i=1}^n X_i$ with i.i.d. $X_i$. We assume that the $X_i$ take values in $Bbb Z^d$, have bounded support and zero mean. For $A subset Bbb Z^d, A ne emptyset$ we def...
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...
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...
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...
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
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 ...

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