Related papers: Stability of trace theorems on the sphere
Based on the multidimensional irreducible paving of De March & Touzi, we provide a multi-dimensional version of the quasi sure duality for the martingale optimal transport problem, thus extending the result of Beiglb\"ock, Nutz & Touzi.…
This article connects the theory of extremal doubly stochastic measures to the geometry and topology of optimal transportation. We begin by reviewing an old question (# 111) of Birkhoff in probability and statistics [4], which is to give a…
We prove Lieb-Thirring inequalities with improved constants on the two-dimensional sphere and the two-dimensional torus. In the one-dimensional periodic case we obtain a simultaneous bound for the negative trace and the number of negative…
We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…
A natural generalization of Krein's theorem to a pair of commuting tuples $\left(H_1^0,H_2^0\right)$ and $\left(H_1,H_2\right)$ of bounded self-adjoint operators in a separable Hilbert space $\mathcal{H}$ with $H_j-H_j^0 = V_j\in…
It is the last paper of a long series. We present the spectral side of the twisted trace formula and its stable version. Using the method of Arthur, we finish the proof of the stabilization of the two sides of this twisted trace formula.
We introduce a new method for proving twisted homological stability, and use it to prove such results for symmetric groups and general linear groups. In addition to sometimes slightly improving the stable range given by the traditional…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
Let $Y$ be a closed $3$-manifold such that all flat $SU(2)$-connections on $Y$ are $non$-$degenerate$. In this article, we prove a Uhlenbeck-type compactness theorem on $Y$ for stable flat $SL(2,\mathbb{C})$ connections satisfying an…
We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a…
We prove local limit theorems for mod-{\phi} convergent sequences of random variables, {\phi} being a stable distribution. In particular, we give two new proofs of a local limit theorem in the framework of mod-phi convergence: one proof…
Let F be a number field and $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of Weil of $\mathrm{Sp}(2n, \mathbb{A}_F)$. We stabilize the elliptic semi-simple terms of the genuine part of trace formula for…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
We prove quantitative bounds on the stability of optimal transport maps and Kantorovich potentials from a fixed source measure $\rho$ under variations of the target measure $\mu$, when the cost function is the squared Riemannian distance on…
This paper contains two main contributions. First, it provides optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev regular in the spatial variable. This estimate is formulated…
We give a short and elementary proof of stability for strong solutions of the spatially homogeneous Landau equation with Coulomb collisions, measured in relative entropy. The argument yields an explicit differential inequality for relative…
Llarull's theorem characterizes the round sphere $S^n$ among all spin manifolds whose scalar curvature is bounded from below by $n(n-1)$. In this paper we show that if the scalar curvature is bounded from below by $n(n-1)-\varepsilon$, the…
In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov-Poisson equation, in the regime where the solutions have bounded…
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…