Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters [PDF]
, 2008 We consider the random walk on supercritical percolation clusters in the d-dimensional Euclidean lattice. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process.
Barlow, Martin, Hambly, Ben
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On the central and local limit theorem for martingale difference sequences [PDF]
, 2004 Let $(\Omega, \A, \mu)$ be a Lebesgue space and $T$ an ergodic measure preserving automorphism on $\Omega$ with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on $\Omega$ with a common non-
Mohamed El Machkouri, Dalibor Volný
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A local limit theorem for a transient chaotic walk in a frozen environment [PDF]
, 2011 This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps.
Lasse Leskelä, Mikko Stenlund
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Local limit theorems for ladder epochs [PDF]
, 2007 Let {S_n, n=0,1,2,...} be a random walk generated by a sequence of i.i.d. random variables X_1, X_2,... and let tau be the first descending ladder epoch. Assuming that the distribution of X_1 belongs to the domain of attraction of an alpha-stable law, we study the asymptotic behavior of P(tau=n).
Vladimir Vatutin, Vitali Wachtel
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Richter’s local limit theorem, its refinement, and related results* [PDF]
Lithuanian Mathematical Journal, 2022 We give a detailed exposition of the proof of Richter’s local limit theorem in a refined form and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).We also discuss
S. Bobkov, G. Chistyakov, F. Götze
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BERRY–ESSEEN BOUND AND LOCAL LIMIT THEOREM FOR THE COEFFICIENTS OF PRODUCTS OF RANDOM MATRICES [PDF]
Journal of the Institute of Mathematics of Jussieu, 2021 Let $\mu $ be a probability measure on $\mathrm {GL}_d(\mathbb {R})$ , and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $\mu $ .
T. Dinh, Lucas Kaufmann, Hao Wu
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A quenched local limit theorem for stochastic flows [PDF]
Journal of Functional Analysis, 2021 We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space.
Alexander Dunlap, Yu Gu
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Local limit theorem in negative curvature [PDF]
Duke Mathematical Journal, 2021 77 pages, 4 figures. The new version has the same structure as the previous ones. Some arguments have been clarified and/or simplified. Typos and some imprecisions have been corrected.
Ledrappier, François, Lim, Seonhee
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Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights [PDF]
Probability theory and related fields, 2020 We establish a quenched local central limit theorem for the dynamic random conductance model on Zd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}
S. Andres +2 more
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A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group [PDF]
Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2020 We prove a zero-one law for the stationary measure for algebraic sets generalizing the results of Furstenberg [13] and Guivarc'h and Le Page [20]. As an application, we establish a local limit theorem for the coefficients of random walks on the general ...
Ion Grama +2 more
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