Related papers: A Bakry-\'Emery criterion for weighted contractivi…
This paper aims to provide some tools coming from functional inequalities to deal with quasi-stationarity for absorbed Markov processes. First, it is shown how a Poincar\'e inequality related to a suitable Doob transform entails exponential…
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…
The Bakry-\'Emery $\Gamma_2$ criterion inequality provides a method for establishing the logarithmic Sobolev inequality. We prove a one-parameter family of weighted Bakry-\'Emery $\Gamma_2$ criterion inequalities which in the limit case…
According to the theory of functional inequalities, a non-symmetric Markov semigroup has better properties than the corresponding symmetric one. For instance, there exist non-symmetric Markov semigroups which are hypercontractive (and thus…
We establish that, for a Markov semi-group, $L^2$ hypocoercivity, i.e. contractivity for a modified $L^2$ norm, implies quantitative deviation bounds for additive functionals of the associated Markov process and exponential integrability of…
The goal of this paper is to give a non-local sufficient condition for generalized Poincar\'e inequalities, which extends the well-known Bakry-Emery condition. Such generalized Poincar\'e inequalities have been introduced by W. Beckner in…
We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the $L^2$-Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together…
It is now well known that curvature conditions \`a la Bakry-Emery are equivalent to contraction properties of the heat semigroup with respect to the classical quadratic Wasserstein distance. However, this curvature condition may include a…
In this paper we intend to give a comprehensive approach of functional inequalities for diffusion processes under some "curvature" assumptions. Our notion of curvature coincides with the usual $\Gamma_2$ curvature of Bakry and Emery in the…
$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are studied.
Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincar\'e or logarithmic Sobolev inequalities. Moreover an alternative method using the…
Inspired by the approach of Ivanisvili and Volberg towards functional inequalities for probability measures with strictly convex potentials, we investigate the relationship between curvature bounds in the sense of Bakry-Emery and local…
Gradient bounds had proved to be a very efficient tool for the control of the rate of convergence to equilibrium for parabolic evolution equations. Among the gradient bounds methods, the celebrated Bakry-\'Emery criterion is a powerful way…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
We study a generalization of the Bakry-\'Emery pointwise gradient estimate for the heat semigroup and its equivalence with some entropic inequalities along the heat flow and Wasserstein geodesics for metric-measure spaces with a suitable…
We investigate in a systematic way hypercontractivity property in Orlicz spaces for Markov semi-groups related to homogeneous and non homogeneous diffusions in $\mathbb{R}^{n}$. We provide an explicit construction of a family of Orlicz…
Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the Bakry-Emery curvature condition, the subordinate semigroup with power $\alpha$ satisfies a…
We consider a coarse version of the marked length spectrum rigidity: given a group with two left invariant metrics, if the marked length spectrum (the translation length function) under the two metrics are the same, then the two metrics are…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
The aim of this paper is to establish weighted Hardy type inequality in a broad family of means. In other words, for a fixed vector of weights $(\lambda_n)_{n=1}^\infty$ and a weighted mean $\mathscr{M}$, we search for the smallest number…