3 citations · 3 across the 3 of their papers we have counts for
5 papers
Geometric implications of fast volume growth and capacity estimates
Tim Jaschek, Mathav Murugan
We obtain connectivity of annuli for a volume doubling metric measure Dirichlet space which satisfies a Poincaré inequality, a capacity estimate and a fast volume growth condition.…
Parabolic Harnack inequality implies the existence of jump kernel
Guanhua Liu, Mathav Murugan
We prove that the parabolic Harnack inequality implies the existence of jump kernel for symmetric pure jump process. This allows us to remove a technical assumption on the jumping…
On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates
Naotaka Kajino, Mathav Murugan
We show that for a strongly local, regular symmetric Dirichlet form over a complete, locally compact geodesic metric space, full off-diagonal heat kernel estimates with walk dimens…
On the length of chains in a metric space
Mathav Murugan
We obtain an upper bound on the minimal number of points in an -chain joining two points in a metric space. This generalizes a bound due to Hambly and Kumagai (1999) for the cas…
Harnack inequalities and Gaussian estimates for random walks on metric measure spaces
Mathav Murugan, Laurent Saloff-Coste
We characterize Gaussian estimates for transition probability of a discrete time Markov chain in terms of geometric properties of the underlying state space. In particular, we show…