Related papers: A sharp log-Sobolev inequality for the multislice

For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of…

We consider consistent diffusion dynamics, leaving the celebrated Hua-Pickrell measures, depending on a complex parameter $s$, invariant. These, give rise to Feller-Markov processes on the infinite dimensional boundary $\Omega$ of the…

We extend Strichartz's uncertainty principle [18] from the setting of the Sobolov space W 1,2 (R) to more general Besov spaces B 1/p p,1 (R). The main result gives an estimate from below of the trace of a function from the Besov space on a…

This note is to study Bourgain's slicing problem following the routes investigated in the last decade. We show that the slicing constant $L_n$ is bounded by $C\log(\log n) $, $n\geq 3$, for some universal constant $C$.

We consider uniformly subelliptic operators on certain unimodular Lie groups of polynomial growth. It was shown by Saloff-Coste and Stroock that classical results of De Giorgi, Nash, Moser, Aronson extend to this setting. It was then…

We obtain a Liouville property for stationary diffusions in random environment which are small, isotropic perturbations of Brownian motion in spacial dimension greater than two. Precisely, we prove that, on a subset of full probability, the…

We show that for the mean zero simple exclusion process in $\mathbb {Z}^d$ and for the asymmetric simple exclusion process in $\mathbb{Z}^d$ for $d\geq3$, the self-diffusion coefficient of a tagged particle is stable when approximated by…

This paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts. If such a subshift satisfies a certain condition, originally introduced by Boshernitzan, every locally constant SL(2,R)-valued…

In this paper, we introduce a generalization of Liu-Yang's weighted norm to linear and to nonlinear hyperbolic equations. Extending a result by Hu and LeFloch for piecewise constant solutions, we establish sharp L1 continuous dependence…

We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a…

We study the sharp constant in the Morrey inequality for fractional Sobolev-Slobodecki\u{\i} spaces on the whole $\mathbb{R}^N$. By generalizing a recent work by Hynd and Seuffert, we prove existence of extremals, together with some…

The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the…

In part 1 (Chapter 2) we present the basic notions of Loewner theory. Here we use a modern form which was developed by F. Bracci, M. Contreras, S. D\'iaz-Madrigal et al. and which can be applied to certain higher dimensional complex…

We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…

We study the quantitative stability of critical points of the fractional Sobolev inequality. We show that, for a non-negative function $u \in \dot H^s(\mathbb R^N)$ whose energy satisfies $$\tfrac{1}{2} S^\frac{N}{2s}_{N,s} \le \|u\|_{\dot…

We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p<2$, while it…

We study small-ball probabilities for the stochastic heat equation with multiplicative noise in the moderate-deviations regime. We prove the existence of a small-ball constant and related it to other known quantities in the literature.…

We establish quantitative estimates for sampling (dominating) sets in model spaces associated with meromorphic inner functions, i.e. those corresponding to de Branges spaces. Our results encompass the Logvinenko-Sereda-Panejah (LSP) Theorem…

The paper is devoted to proving Allard-Michael-Simon-type $L^p$-Sobolev inequalities $(p>1)$ with explicit constants in the setting of Euclidean minimal submanifolds of arbitrary codimension. Our results require separate discussions for the…

We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random…