Results 1 
3 of
3
SubGaussian estimates of heat kernels on infinite graphs
 Duke Math. J
, 2000
"... We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay. ..."
Abstract

Cited by 30 (10 self)
 Add to MetaCart
We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.
Harnack inequalities and subGaussian estimates for random walks
 Math. Annalen
, 2002
"... We show that a fiparabolic Harnack inequality for random walks on graphs is equivalent, on one hand, to so called fiGaussian estimates for the transition probability and, on the other hand, to the conjunction of the elliptic Harnack inequality, the doubling volume property, and the fact that the m ..."
Abstract

Cited by 29 (6 self)
 Add to MetaCart
We show that a fiparabolic Harnack inequality for random walks on graphs is equivalent, on one hand, to so called fiGaussian estimates for the transition probability and, on the other hand, to the conjunction of the elliptic Harnack inequality, the doubling volume property, and the fact that the mean exit time in any ball of radius R is of the order R . The latter condition can be replaced by a certain estimate of a resistance of annuli.
Random fractal dendrites David Croydon
"... First, I would like to thank my supervisor, Dr. Ben Hambly, who has managed to keep my research on track for the last three years. When we first met, he provided me with a list of things to think about, and this thesis manages to answer the first of the problems on that list. For this initial inspir ..."
Abstract
 Add to MetaCart
First, I would like to thank my supervisor, Dr. Ben Hambly, who has managed to keep my research on track for the last three years. When we first met, he provided me with a list of things to think about, and this thesis manages to answer the first of the problems on that list. For this initial inspiration and his invaluable guidance throughout, I will always be grateful. During my time in Oxford, the Mathematical Institute has been an excellent place in which to work, and I have no doubt benefited from the many activities of the Stochastic Analysis Research Group, so many thanks to Prof. Terry Lyons and everyone else who has contributed to making these things happen. I would particularly like to thank all the people with whom I have spent time in the office for providing me with some much needed support (I thought this was more polite than “distraction”) in my daily life. Last, but by no means least, I would like to thank my friends, family, and