Related papers: On Harnack inequalities and optimal transportation
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 comparable? We address this question when the diffusion…
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities…
In this paper necessary and sufficient conditions are presented for heat kernel upper bounds for random walks on weighted graphs. Several equivalent conditions are given in the form of isoperimetric inequalities.
We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.
We prove a global Li-Yau inequality for a general Markov semigroup under a curvature-dimension condition. This inequality is stronger than all classical Li-Yau type inequalities known to us. On a Riemannian manifold, it is equivalent to a…
To study the reflecting diffusion processes on manifolds with boundary, some new curvature operators are introduced by using the Bakry-Emery curvature and the second fundamental form. As applications, the gradient estimates, log-Harnack…
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…
For the Neumann heat flow on nonconvex Riemannian domains $D\subset M$, we provide sharp gradient estimates and transport estimates with a novel $\sqrt t$-dependence, for instance, $$\text{Lip}( P^D_tf)\le e^{2S \,…
A quadratic optimal transport metric on the set of probability measure over $\R^2$ is introduced. The quadratic cost is given by the euclidean norm on $\R^2$ associated to some well chosen symmetric positive matrix, which makes the metric…
Heat transfer in liquids is a very challenging problem as it combines the competing effect of high frequency oscillations, which dominate liquid heat capacity, and diffusive motion, which enables transport macroscopic flow. This issue is…
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities for positive solutions of backward heat-type equations with potentials (including the…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
We introduce a semigroup framework for Laplacians on directed hypergraphs, extending the classical heat flow models on graphs and establishing hypergraphs as prototypical models for non-Markovian diffusion. We apply spectral surgery methods…
In this note, we concentrate on the sub-Laplace on the nilpotent Lie group of rank two, which is the infinitesimal generator of the diffusion generated by $n$ Brownian motions and their $\frac{n(n-1)}2$ L\'evy area processes, which is the…
We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including…
We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the…