Integral Varadhan formula for non-linear heat flow

Autor:	Ohta, Shin-ichi, Suzuki, Kohei
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Functional Analysis Mathematics - Metric Geometry
Druh dokumentu:	Working Paper
Popis:	We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishing a Varadhan-type formula for non-linear semigroups. We do not assume the reversibility of the metric, and the distance function can be asymmetric. Within this generality, we reveal that the probabilistic interpretation is well-suited for our formula; the probability that a particle starting from a set $A$ can be found in another set $B$ describes the distance from $A$ to $B$. One side of the estimates (the upper bound of the probability) is also established in the nonsmooth setting of infinitesimally strictly convex metric measure spaces satisfying the local Sobolev-to-Lipschitz property. Comment: 24 pages, comments are welcomed!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.04102 Zobrazit plný text záznamu View this record from Arxiv