Related papers: Dimension-independent functional inequalities by t…
We consider sub-Riemannian manifolds which are homogeneous spaces equipped with a natural sub-Riemannian structure induced by a transitive action by a Lie group. In such a setting, the corresponding sub-Laplacian is not an elliptic but a…
We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles $N$. Our proof proceeds by establishing the existence of a Lipschitz…
In this paper, we use the Carnot-Caratheodory distance from sub-Riemanian geometry to prove entropy decay estimates for all finite dimensional symmetric quantum Markov semigroups. This estimate is independent of the environment size and…
We study the relationship between functional inequalities for a Markov kernel on a metric space $X$ and inequalities of transportation distances on the space of probability measures $\mathcal{P}(X)$. Extending results of Luise and Savar\'e…
We study score-based diffusion modelling in infinite-dimensional separable Hilbert spaces through Malliavin calculus, extending the analysis of generative models beyond the finite-dimensional setting. The forward diffusion process is…
Explicit sufficient conditions on the hypercontractivity are presented for two classes of functional stochastic partial differential equations driven by, respectively, non-degenerate and degenerate Gaussian noises. Consequently, these…
We analyze the constant step size subgradient method on nonsmooth, nonconvex functions. We identify geometric assumptions on the objective function under which i) its domain admits a partition (stratification) into smooth manifolds (strata)…
We study functional inequalities for Markov chains on discrete spaces with entropic Ricci curvature bounded from below. Our main results are that when curvature is non-negative, but not necessarily positive, the spectral gap, the Cheeger…
We consider a parabolic equation driven by a nonlinear diffusive operator and we obtain a gradient estimate in the domain where the equation takes place. This estimate depends on the structural constants of the equation, on the geometry of…
We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by these flows persist under $C^1$ perturbation. In particular, we…
We consider a problem of covariance estimation from a sample of i.i.d. high-dimensional random vectors. To avoid the curse of dimensionality, we impose an additional assumption on the structure of the covariance matrix $\Sigma$. To be more…
We prove gradient estimates for transition Markov semigroups $(P_t)$ associated to SDEs driven by multiplicative Brownian noise having possibly unbounded $C^1$-coefficients, without requiring any monotonicity type condition. In particular,…
We analyze infinite-dimensional non-linear degenerate stochastic differential equations with multiplicative noise. First, essential m-dissipativity of their associated Kolmogorov backward generators on $L^2(\mu^{\Phi})$ defined on smooth…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
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 use the inverse pressure concept to estimate the stable dimension for hyperbolic non-invertible maps which are conformal in the stable fibers. The non-invertible case is different than the diffeomorphism case. In particular we show that…
We prove that in the context of general Markov semigroups Beckner inequalities with constants separated from zero as $p\to 1^+$ are equivalent to the modified log Sobolev inequality (previously only one implication was known to hold in this…
We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions…
Let $X$ be a separable Hilbert space endowed with a non-degenerate centred Gaussian measure $\gamma$ and let $\lambda_1$ be the maximum eigenvalue of the covariance operator associated with $\gamma$. The associated Cameron--Martin space is…
In this paper we consider the general structure of irreducible tensor representations of the Poincare group of arbitrary dimension with multiple sets of Lorentz indices and different ways to construct them from basic elements (Lorentz…