Random walks in random environments without ellipticity
نویسندگان
چکیده
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 ...
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Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium (for a general reference see, e.g., Hughes (1995)). However, in many practical cases the medium where the system evolves is highly irregular, due to factors such as defects, impurities, fluctuations etc. It is natural to model such irr...
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Random walks in random environments (RWRE’s) and their diffusion analogues have been a source of surprising phenomena and challenging problems, especially in the non-reversible situation, since they began to be studied in the 70’s. We review the model, available results and techniques, and point out several gaps in the understanding of these processes. 2000 Mathematics Subject Classification: 6...
متن کاملRandom Walks in Degenerate Random Environments
We study the asymptotic behaviour of random walks in i.i.d. random environments on Z. The environments need not be elliptic, so some steps may not be available to the random walker. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience, and in 2-dimensions the existence of a deterministic limiting velocity. We prove a monotonicity result for th...
متن کاملa 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 no...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2013
ISSN: 0304-4149
DOI: 10.1016/j.spa.2013.01.007