Related papers: Transportation Cost Inequalities for Neutral Funct…
We review here some recent results by the authors, and various coauthors, on (weak,super) Poincar\'e inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite simple and efficient technique:…
We propose a simple scheme that describes accurately essential non-equilibrium effects in nanoscale electronics devices using equilibrium transport theory. The scheme, which is based on the alignment and dealignment of the junction…
We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport…
For a functional defined on the class of closed one-dimensional connected subsets of ${\mathbb R}^n$ we consider the corresponding minimization problem and we give suitable first order necessary conditions of optimality. The cases studied…
In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
Explicit energy-transport equations for the spinorial carrier transport in ferromagnetic semiconductors are calculated from a general spin energy-transport system that was derived by Ben Abdallah and El Hajj from a spinorial Boltzmann…
Structured equations are a standard modeling tool in mathematical biology. They areintegro-differential equations where the unknown depends on one or several variables, representing the state or phenotype of individuals. A large literature…
We shall prove new contraction properties of general transportation costs along nonnegative measure-valued solutions to Fokker-Planck equations in $R^d$, when the drift is a monotone (or $\lambda$-monotone) operator. A new duality approach…
In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) a exponential approximation argument to investigate large deviations for neutral stochastic functional differential…
A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
This paper is devoted to study a class of stochastic Volterra equations associated with fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality for the Gibbs measure on…
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
For stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H>1/2$, Harnack type inequalities are established by constructing a coupling with unbounded time-dependent drift. These inequalities are applied…
Transport properties of 2D materials especially close to their boundary has received much attention after the successful fabrication of graphene and other fascinating materials afterwards. While most previous work is devoted to the…