Fabrice Baudoin
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View article: Topology and bottom spectrum of transversally negatively curved foliations
Topology and bottom spectrum of transversally negatively curved foliations Open
We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a s…
View article: Sub-Laplacian comparison theorems on Riemannian foliations with minimal leaves and applications
Sub-Laplacian comparison theorems on Riemannian foliations with minimal leaves and applications Open
We prove comparison theorems for the horizontal Laplacian of the Riemannian distance in the context of Riemannian foliations with minimal leaves. This general framework generalizes previous works and allow us to consider the sub-Laplacian …
View article: Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds
Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds Open
View article: Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees
Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees Open
We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform volume growth condition. Using the intrinsic geodesic structu…
View article: Orlicz-Sobolev embeddings and heat kernel based Besov classes
Orlicz-Sobolev embeddings and heat kernel based Besov classes Open
This paper investigates functional inequalities involving Besov spaces and functions of bounded variation, when the underlying metric measure space displays different local and global structures. Particular focus is put on the $L^1$ theory…
View article: Comparison theorems on H-type sub-Riemannian manifolds
Comparison theorems on H-type sub-Riemannian manifolds Open
View article: Brownian motion and stochastic areas on complex full flag manifolds
Brownian motion and stochastic areas on complex full flag manifolds Open
We show that the Brownian motion on the complex full flag manifold can be represented by a matrix-valued diffusion obtained from the unitary Brownian motion. This representation actually leads to an explicit formula for the characteristic …
View article: Weighted Besov spaces on Heisenberg groups and applications to the Parabolic Anderson model
Weighted Besov spaces on Heisenberg groups and applications to the Parabolic Anderson model Open
This article aims at a proper definition and resolution of the parabolic Anderson model on Heisenberg groups $\mathbf{H}_{n}$. This stochastic PDE is understood in a pathwise (Stratonovich) sense. We consider a noise which is smoother than…
View article: Convergence to equilibrium for hypoelliptic non-symmetric Ornstein-Uhlenbeck-type operators
Convergence to equilibrium for hypoelliptic non-symmetric Ornstein-Uhlenbeck-type operators Open
We study a generalized curvature-dimension inequality which is suitable for sub-Riemannian Ornstein-Uhlenbeck-type operators and deduce convergence to equilibrium in the and entropic sense. The main difficulty is that the operators we con…
View article: Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds
Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds Open
We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in space parameterized by a regularity parameter $α$, which we u…
View article: On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations
On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations Open
We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from w…
View article: Heat kernel gradient estimates for the Vicsek set
Heat kernel gradient estimates for the Vicsek set Open
We prove pointwise and gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hodge semigroup in that setting and prove estimates for its kernel.
View article: Fractional stable random fields on the Sierpiński gasket
Fractional stable random fields on the Sierpiński gasket Open
We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as (−Δ)−sWK,α, where Δ is the Laplace operator on the gasket and WK,α is a stable random measur…
View article: Korevaar–Schoen–Sobolev spaces and critical exponents in metric measure spaces
Korevaar–Schoen–Sobolev spaces and critical exponents in metric measure spaces Open
We survey, unify and present new developments in the theory of Korevaar–Schoen–Sobolev spaces on metric measure spaces. While this theory coincides with those of Cheeger and Shanmugalingam if the space is doubling and supports a Poincaré i…
View article: The indifference value of the weak information
The indifference value of the weak information Open
We propose indifference pricing to estimate the value of the weak information. Our framework allows for tractability, quantifying the amount of additional information, and permits the description of the smallness and the stability with res…
View article: Topology and bottom spectrum of transversally negatively curved foliations
Topology and bottom spectrum of transversally negatively curved foliations Open
We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a s…
View article: Dimension-independent functional inequalities by tensorization and projection arguments
Dimension-independent functional inequalities by tensorization and projection arguments Open
We study stability under tensorization and projection-type operations of gradient-type estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation-type inequalities obtained by F. Baudoin and N.…
View article: Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals
Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals Open
We investigate regularity properties of some non-local equations defined on Dirichlet spaces equipped with sub-gaussian estimates for the heat kernel associated to the generator. We prove that weak solutions for homogeneous equations invol…
View article: Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces
Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces Open
This paper studies properties of $Γ$-limits of Korevaar-Schoen $p$-energies on a Cheeger space. When $p>1$, this kind of limit provides a natural $p$-energy form that can be used to define a $p$-Laplacian, and whose domain is the Newtonian…
View article: Fractional stable random fields on the Sierpiński gasket
Fractional stable random fields on the Sierpiński gasket Open
We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as $(-Δ)^{-s} W_{K,α}$, where $Δ$ is the Laplace operator on the gasket and $W_{K,α}$ is a stable random measure. Both Neumann a…
View article: Parabolic Anderson model in bounded domains of recurrent metric measure spaces
Parabolic Anderson model in bounded domains of recurrent metric measure spaces Open
A metric measure space equipped with a Dirichlet form is called recurrent if its Hausdorff dimension is less than its walk dimension. In bounded domains of such spaces we study the parabolic Anderson models \[ \partial_{t} u(t,x) = Δu(t,x)…
View article: Heat kernel gradient estimates for the Vicsek set
Heat kernel gradient estimates for the Vicsek set Open
We prove pointwise and $L^p$ gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hodge semigroup in that setting and prove estimates for its ke…
View article: Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise
Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise Open
For a family of infinite-dimensional diffusions with degenerate noise, we develop a modified $Γ$ calculus on finite-dimensional projections of the equation in order to produce explicit functional inequalities that can be scaled to infinite…
View article: Yet another heat semigroup characterization of BV functions on Riemannian manifolds
Yet another heat semigroup characterization of BV functions on Riemannian manifolds Open
This paper provides a characterization of functions of bounded variation (BV) in a compact Riemannian manifold in terms of the short time behavior of the heat semigroup. In particular, the main result proves that the total variation of a f…
View article: Oscillations of BV measures on unbounded nested fractals
Oscillations of BV measures on unbounded nested fractals Open
Motivated by recent developments in the theory of bounded variation functions on unbounded nested fractals, this paper studies the exact asymptotics of functionals related to the total variation measure associated with unions of n -cells. …
View article: Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions
Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions Open
View article: Covariance inequalities for convex and log-concave functions
Covariance inequalities for convex and log-concave functions Open
Extending results of Harg{é} and Hu for the Gaussian measure, we prove inequalities for the covariance Cov$_μ(f, g)$ where $μ$ is a general product probability measure on $\mathbb{R}^d$ and $f,g: \mathbb{R}^d \to \mathbb{R}$ satisfy some c…
View article: Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies
Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies Open
This paper establishes sufficient general conditions for the existence of Mosco limits of Korevaar-Schoen $L^2$ energies, first in the context of Cheeger spaces and then in the context of fractal-like spaces with walk dimension greater tha…
View article: Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling
Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling Open
On Sasakian manifolds with their naturally occurring sub-Riemannian structure, we consider parallel and mirror maps along geodesics of a taming Riemannian metric. We show that these transport maps have well-defined limits outside the sub-R…
View article: Stochastic areas, Horizontal Brownian Motions, and Hypoelliptic Heat Kernels
Stochastic areas, Horizontal Brownian Motions, and Hypoelliptic Heat Kernels Open
The monograph is devoted to the study of stochastic area functionals of Brownian motions and of the associated heat kernels on Lie groups and Riemannian manifolds. It is essentially self-contained and as such can serve as a textbook on the…