4 citations · 7 across the 4 of their papers we have counts for
8 papers · 1 filter
On the comparison between jump processes and subordinated diffusions
Guanhua Liu, Mathav Murugan
Given a symmetric diffusion process and a jump process on the same underlying space, is there a subordinator such that the jump process and the subordinated diffusion processes are…
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…
A note on heat kernel estimates, resistance bounds and Poincaré inequality
Mathav Murugan
Sub-Gaussian heat kernel estimates are typical of fractal graphs. We show that sub-Gaussian estimates on graphs follow from a Poincaré inequality, capacity upper bound, and a slow…