Related papers: Transportation inequalities for Markov kernels and…
We develop a unified geometric framework for nonparametric estimation based on the notion of Twin Kernel Spaces, defined as orbits of a reproducing kernel under a group action. This structure induces a family of transported RKHS geometries…
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 prove that for a probability measure on $\mathbb{R}^n$, the Poincar\'e inequality for convex functions is equivalent to the weak transportation inequality with a quadratic-linear cost. This generalizes recent results by Gozlan et al. and…
We study distributions of meeting times for finite symmetric Markov chains. For Markov kernels defined on large state spaces which satisfy certain weak inhomogeneity in return probabilities of points up to large numbers of steps, we obtain…
We study a family of fractional integral operators defined in $\mathbb{R}^3$ whose kernels are distributions associated with Zygmund dilations: $(x_1, x_2, x_3) \rightarrow (\delta_1 x_1, \delta_2 x_2, \delta_1\delta_2 x_3)$ for…
On a doubling metric measure space $(M,d,\mu)$ endowed with a "carr\'e du champ", let $\mathcal{L}$ be the associated Markov generator and $\dot L^{p}_\alpha(M,\mathcal{L},\mu)$ the corresponding homogeneous Sobolev space of order…
We establish transportation cost inequalities, with respect to the uniform and $L_2$-metric, on the path space of continuous functions, for laws of solutions of stochastic differential equations with reflections. We also consider the case…
We investigate the use of a certain class of functional inequalities known as weak Poincar\'e inequalities to bound convergence of Markov chains to equilibrium. We show that this enables the straightforward and transparent derivation of…
We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this…
We construct a family of infinite-dimensional reduced Heisenberg groups which can be viewed as infinite-dimensional homogeneous spaces. Such a space is an analogue of finite-dimensional reduced Heisenberg groups in infinite dimensions. We…
We relate transport-entropy inequalities to the study of critical points of functionals defined on the space of probability measures. This approach leads in particular to a new proof of a result by Otto and Villani [43] showing that the…
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently…
We introduce a H\"older regularity condition for harmonic functions on metric measure spaces and prove that, under a slow volume regular condition and an upper heat kernel estimate, the H\"older regularity condition, the weak Bakry-\'Emery…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
The main goal of this paper is to generalize the Sobolev-type inequalities given by Guo-Phong-Song-Sturm and Guedj-T\^o from the case of functions to the framework of twisted differential forms. To this end, we establish certain estimates…
We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of well known two-sided Gaussian heat kernel…
The hypercontractivity is proved for the Markov semigroup associated to a class of finite/infinite dimensional stochastic Hamiltonian systems. Consequently, the Markov semigroup is exponentially convergent to the invariant probability…
In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost. This class of inequalities has been introduced in the recent…
We obtain Sobolev inequalities for the Schrodinger operator -\Delta-V, where V has critical behaviour V(x)=((N-2)/2)^2|x|^{-2} near the origin. We apply these inequalities to obtain pointwise estimates on the associated heat kernel,…
Though Adams and Hardy-Adams inequalities can be extended to general symmetric spaces of noncompact type fairly straightforwardly by following closely the systematic approach developed in our early works on real and complex hyperbolic…