Disconnection, random walks, and random interlacements
نویسندگان
چکیده
منابع مشابه
A lower bound for disconnection by random interlacements
We consider the vacant set of random interlacements on Z, d ≥ 3, in the percolative regime. Motivated by the large deviation principles recently obtained in [13], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates t...
متن کاملRandom walks on discrete cylinders with large bases and random interlacements
Following the recent work of Sznitman [20], we investigate the microscopic picture induced by a random walk trajectory on a cylinder of the form GN ×Z, where GN is a large finite connected weighted graph, and relate it to the model of random interlacements on infinite transient weighted graphs. Under suitable assumptions, the set of points not visited by the random walk until a time of order |G...
متن کاملRandom Walks and Random Permutations
A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version of the model can be determined to be the same as the scaled distribution of the eigenvalues at the soft edge of the GUE. The scaling of the distribution gives...
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 ...
متن کاملRandom Walks in Random Environments
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2015
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-015-0676-y