Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations
Probability
2024-10-30 v2 Metric Geometry
Spectral Theory
Abstract
We show that for ultracontractive irreducible Dirichlet metric measure spaces, the Dirichlet spectrum is discrete for a restriction to any connected open set without any assumption on regularity of the boundary. The main applications include small deviations for the corresponding Hunt process and large time asymptotics for the generalized heat content. Our examples include Riemannian and sub-Riemannian manifolds, as well as non-smooth and fractal spaces.
Cite
@article{arxiv.2409.07425,
title = {Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations},
author = {Marco Carfagnini and Maria Gordina and Alexander Teplyaev},
journal= {arXiv preprint arXiv:2409.07425},
year = {2024}
}
Comments
Minor changes, added references