 

Mathav Murugan and Laurent SaloffCoste
Transition probability estimates for long range random walks view print


Published: 
August 12, 2015 
Keywords: 
long range random walks; heat kernel estimates; heavytailed 
Subject: 
60J10, 60J75, 60J15 


Abstract
Let (M,d,μ) be a uniformly discrete metric measure space satisfying space homogeneous volume doubling condition. We consider discrete time Markov chains on M symmetric with respect to μ and whose onestep transition density is
comparable to
(V_{h}(d(x,y)) ϕ(d(x,y))^{1},
where ϕ is a positive continuous regularly varying function with index β ∈ (0,2) and V_{h} is the homogeneous volume growth function.
Extending several existing work by other authors, we prove global upper and lower bounds for nstep transition probability density that are sharp up to constants.


Acknowledgements
Both authors were partially supported by NSF grants DMS 1004771 and DMS 1404435


Author information
Mathav Murugan:
Department of Mathematics, University of British Columbia and Pacific Institute for the Mathematical Sciences, Vancouver, BC V6T 1Z2, Canada.
mathav@math.ubc.ca
Laurent SaloffCoste:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA.
lsc@math.cornell.edu

