scholarly journals Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights

2021 ◽  
Vol 179 (3-4) ◽  
pp. 1145-1181 ◽  
Author(s):  
Sebastian Andres ◽  
Alberto Chiarini ◽  
Martin Slowik
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Local Limit Theorem ◽  
Time Dependent ◽  
Moment Condition ◽  
Difference Operators ◽  
Random Conductance Model ◽  
Local Central Limit Theorem ◽  
Random Conductance

AbstractWe establish a quenched local central limit theorem for the dynamic random conductance model on $${\mathbb {Z}}^d$$ Z d only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show Hölder continuity estimates for solutions to the heat equation for discrete finite difference operators in divergence form with time-dependent degenerate weights. The proof is based on De Giorgi’s iteration technique. In addition, we also derive a quenched local central limit theorem for the static random conductance model on a class of random graphs with degenerate ergodic weights.

scholarly journals Quenched local central limit theorem for random walks in a time-dependent balanced random environment

2021 ◽  
Author(s):  
Jean-Dominique Deuschel ◽  
Xiaoqin Guo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Random Environment ◽  
Transition Probabilities ◽  
Time Dependent ◽  
Upper And Lower Bounds ◽  
Negative Moment ◽  
Local Central Limit Theorem

AbstractWe prove a quenched local central limit theorem for continuous-time random walks in $${\mathbb {Z}}^d, d\ge 2$$ Z d , d ≥ 2 , in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian upper and lower bounds for quenched and (positive and negative) moment estimates of the transition probabilities and asymptotics of the discrete Green’s function.

A central limit theorem for conditionally centred random fields with an application to Markov fields

1998 ◽  
Vol 35 (03) ◽  
pp. 608-621
Author(s):  
Francis Comets ◽  
Martin Janžura
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Markov Random Fields ◽  
Moment Condition ◽  
Markov Random ◽  
Pseudo Likelihood ◽  
Strict Positivity ◽  
Markov Fields

We prove a central limit theorem for conditionally centred random fields, under a moment condition and strict positivity of the empirical variance per observation. We use a random normalization, which fits non-stationary situations. The theorem applies directly to Markov random fields, including the cases of phase transition and lack of stationarity. One consequence is the asymptotic normality of the maximum pseudo-likelihood estimator for Markov fields in complete generality.

A local central limit theorem for triangles in a random graph

2016 ◽  
Vol 48 (4) ◽  
pp. 732-750 ◽  
Author(s):  
Justin Gilmer ◽  
Swastik Kopparty
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Graph ◽  
Local Central Limit Theorem

The almost sure local central limit theorem for the product of partial sums

2011 ◽  
Vol 121 (2) ◽  
pp. 217-228 ◽  
Author(s):  
ZHICHAO WENG ◽  
ZUOXIANG PENG ◽  
SARALEES NADARAJAH
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Partial Sums ◽  
Local Central Limit Theorem
Sign in / Sign up

Export Citation Format

Share Document