Random Walks in Random Environment
نویسندگان
چکیده
My main research interest is in theoretical and applied probability mainly focusing on discrete problems arising out of combinatorics, statistical physics and computer science. In particular I am interested in random graphs, probability on tress, combinatorial optimization and statistical physics problems, recursive distributional equations, branching random walks, percolation theory, interacting particle systems, Markov chains and their mixing behavior, random walks in random environment, urn models. I also keep strong interest in theoretical statistics and probability questions arising out of it. The following three sections describes my research work, current projects and future plans. The topics are arranged alphabetically.
منابع مشابه
A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملLarge Deviations for Random Walks in a Mixing Random Environment and Other (Non-Markov) Random Walks
We extend a recent work by S. R. S. Varadhan [8] on large deviations for random walks in a product random environment to include more general random walks on the lattice. In particular, some reinforced random walks and several classes of random walks in Gibbs fields are included. c © 2004 Wiley Periodicals, Inc.
متن کاملQuenched invariance principle for random walks in balanced random environment
We consider random walks in a balanced random environment in Z , d ≥ 2. We first prove an invariance principle (for d ≥ 2) and the transience of the random walks when d ≥ 3 (recurrence when d = 2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for ran...
متن کاملTransient random walks on a strip in a random environment
We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid in [4]. We derive a strong law of large numbers for the random walks in a general ergodic setup and obtain an annealed central limit theorem in the case of uniformly mixing environments. In addition, we prove that the law of the “environment viewed from the position of the...
متن کاملSystems of One-dimensional Random Walks in a Common Random Environment
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed vP . We give upper bounds on the quenched probability that at least one of the random walks started in the interval [An, Bn] has traveled a distance of less than (vP − ε)n. This leads to both a uniform law of large numbers an...
متن کاملBranching random walks in random environment on Cayley graphs
We review some recent results concerning recurrence and transience for branching random walks in random environment on ddimensional lattices and on trees. We obtain some generalizations of these results for the case when the branching random walk in random environment takes place on arbitrary infinite connected Cayley graph.
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