Large deviations for simple random walk on percolations with long-range correlations
نویسنده
چکیده
We show quenched large deviations for the simple random walk on percolation models with long-range correlations defined by Drewitz, Ráth and Sapozhnikov [3], which contain supercritical Bernoulli percolations, random interlacements, the vacant set of random interlacements and the level set of the Gaussian free field. Our result is an extension of Kubota’s result [8] for supercritical Bernoulli percolations.
منابع مشابه
Percolations on random maps I: half-plane models
We study Bernoulli percolations on random lattices of the half-plane obtained as local limit of uniform planar triangulations or quadrangulations. Using the characteristic spatial Markov property or peeling process [5] of these random lattices we prove a surprisingly simple universal formula for the critical threshold for bond and face percolations on these graphs. Our techniques also permit us...
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 کاملNovel Method for Generating Long-Range Correlations
A b s t r a c t We propose an algorithm to generate a sequence of numbers with long-range power-law correlations which is well-suited for large systems. Starting with a set of random uncorrelated variables, we modify its Fourier transform to get a new sequence with longrange correlations. By mapping the variables to a one dimensional random walk problem we find analytical and numerical evidence...
متن کاملSimulation of a directed random-walk model: the effect of pseudo-random-number correlations
We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorit...
متن کاملScaling in the market of futures
The price time series of the Italian government bonds (BTP) futures is studied by means of scaling concepts originally developed for random walks in statistical physics. The series of overnight price di erences is mapped onto a one-dimensional random walk: the bond walk. The analysis of the root mean square uctuation function and of the auto-correlation function indicates the absence of both sh...
متن کامل