scholarly journals Lower Gaussian heat kernel bounds for the random conductance model in a degenerate ergodic environment

2021 ◽  
Author(s):  
Sebastian Andres ◽  
Noah Halberstam
Keyword(s):  
Heat Kernel ◽  
Random Conductance Model ◽  
Kernel Bounds ◽  
Random Conductance

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 Erratum to “Global heat kernel bounds via desingularizing weights”

2005 ◽  
Vol 220 (1) ◽  
pp. 238-239
Author(s):  
Pierre D. Milman ◽  
Yu.A. Semenov
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds

scholarly journals Heat kernel bounds on manifolds with cusps

1987 ◽  
Vol 75 (2) ◽  
pp. 311-322 ◽  
Author(s):  
E.B Davies ◽  
N Mandouvalos
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds

scholarly journals Surgery of the Faber–Krahn inequality and applications to heat kernel bounds

2016 ◽  
Vol 131 ◽  
pp. 243-272 ◽  
Author(s):  
Alexander Grigor’yan ◽  
Laurent Saloff-Coste
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds ◽  
Krahn Inequality

scholarly journals Evolving sets, mixing and heat kernel bounds

2005 ◽  
Vol 133 (2) ◽  
pp. 245-266 ◽  
Author(s):  
B. Morris ◽  
Yuval Peres
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds
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