Related papers: Transportation cost inequalities for diffusions un…
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward…
By using a split argument due to [1], the transportation cost inequality is established on the free path space of Markov processes. The general result is applied to stochastic reaction diffusion equations with random initial values.
We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional…
In this note, we investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave solutions in a homogeneous Lipschitz sense. We derive…
For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
The mass flux of a low-density granular binary mixture obtained previously by solving the Boltzmann equation by means of the Chapman-Enskog method is considered further. As in the elastic case, the associated transport coefficients $D$,…
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
Diffusion processes are studied theoretically for the case where the diffusion coefficient is itself a time and position dependent random function. We investigate how inhomogeneities and fluctuations of the diffusion coefficient affect the…
We present a noncommutative optimal transport framework for quantum channels acting on von Neumann algebras. Our central object is the Lipschitz cost measure, a transportation-inspired quantity that evaluates the minimal cost required to…
We prove a new sample complexity result for divergence regularized optimal transport. Our bound holds for probability measures on~$\mathbb{R}^d$ with exponential tail decay and for radial cost functions that satisfy a local Lipschitz…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for…
We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives…
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a unified treatment of the available literature along with some…
In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincar\'{e} inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of…
We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also…
We provide non-asymptotic bounds and asymptotic limits for convex transport costs between the distribution of partial sums of independent and identically distributed square integrable and centered random variables and the normal…
We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…