The local central limit theorem for Stirling numbers of the second kind and an estimate for bell numbers

1981 ◽  
pp. 321-330 ◽  
Author(s):  
V. V. Menon
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stirling Numbers ◽  
Bell Numbers ◽  
Local Central Limit Theorem

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.

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