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

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.

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

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.

Local central limit theorem

2012 ◽  
pp. 21-71
Author(s):  
Gregory F. Lawler ◽  
Vlada Limic
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Local Central Limit Theorem
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