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Emanuel Milman29/05/2023 14:00
The classical isoperimetric inequality in Euclidean space R^n states that among all sets of prescribed volume, the Euclidean ball minimizes surface area. One may similarly consider isoperimetric problems for more general metric-measure spaces, such as on the n-sphere S^n and on n-dimensional Gaussian space G^n (i.e. R^n endowed with the standard Gaussian measure). Furthermore, one may consider...
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Marta Strelecka29/05/2023 14:45
We consider the structured Gaussian matrix G_A=(a_{ij}g_{ij}), where g_{ij}'s are independent standard Gaussian variables. The exact behavior of the spectral norm of the structured Gaussian matrix is known due to the result of Latala, van Handel, and Youssef from 2018. We are interested in two-sided bounds for the expected value of the norm of G_A treated as an operator from l_p^n to l_q^m. We...
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Yaozhong Qiu29/05/2023 16:10
We review some progress in the study of generalised Bakry-Émery calculi, and then discuss some recent developments concerning the particular case of the Bakry-Émery calculus associated to multiplication operators. We provide a connection with Hardy inequalities, a sufficient criterion thereof, and some typical examples.
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Esther Bou Dagher29/05/2023 16:55
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Arnaud Marsiglietti30/05/2023 09:45
In this talk, we will discuss an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise. We will also discuss an asymptotic behavior for Rényi entropies along convolutions in the central limit theorem. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.
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Michael Goldman30/05/2023 11:10
In this talk I will present some recent progress in the understanding of the optimal matching problem. Since it is one of the simplest (random) combinatorial problem and because of its numerous connections to theoretical physics, computer sciences and of course probability theory, this problem has attracted a lot of attention from various communities. One of the most striking properties of...
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James Melbourne30/05/2023 11:55
A sequence of numbers is considered log-concave with respect to another when the ratio of the two is log-concave. Such relationships arise naturally in diverse fields of study. Examples include the following. The intrinsic volume sequence associated to a convex body, which is log-concave with respect to the probabilities of a Poisson distribution. The confirmation of the strong Mason...
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Galyna Livshyts30/05/2023 14:00
We establish the equality cases in the celebrated Gaussian B-inequality of Cordero-Erasquin, Fradelizi and Maurey: we show that the equality only holds when the corresponding symmetric convex body is either the whole space or has an empty interior. Furthermore, we derive a stability version with a sharp rate (in some sense). Moreover, we establish equality cases in the strong B-inequality...
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Alexandros Eskenazis30/05/2023 14:45
We shall discuss the state of the art on the problem of identifying the volume maximizing and minimizing hyperplane sections of p-balls. Specifically, we will present a recent work with P. Nayar (Warsaw) and T. Tkocz (CMU) identifying the volume maximizing section for p greater than a universal constant.
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Götze30/05/2023 16:10
We review previous joint results with S. Bobkov and G. Chistyakov for the central limit theorem in the R\'enyi divergence distances of order larger than one and discuss recent progress for the case of infinite order as well as related questions concerning classes of strongly sub-Gaussian distributions.
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Ramon van Handel31/05/2023 09:45
The concentration of measure phenomenon asserts that in a remarkably broad
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range of situations, nonlinear functions of many random variables are well
concentrated around their means. A question that arises naturally in
probability theory, functional analysis, metric geometry, and geometric
group theory is whether there exist analogous phenomena for vector-valued
functions, i.e., taking... -
Maud Szusterman31/05/2023 11:10
I. Soprunov and A. Zvavitch have shown some mixed volume inequalities for the simplex, which translate algebraic inequalities known as Bezout inequalities. Together with C. Saroglou, they have proven in 2018 that this family of inequalities characterizes the simplex among all polytopes, and conjecturally the characterization would hold among all convex bodies in R^n. These three authors have...
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Krzysztof Oleszkiewicz31/05/2023 11:55
A century after the Khinchine inequalities were proven, most of the optimal constants in them are still unknown, but there is a slow, gradual progress in understanding their asymptotic behaviour. I will report on some recent result in this direction.
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Rafal Latala31/05/2023 14:00
We present a Chevet-type inequality for subsexpontial Weibull processes and show how
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it may be applied to derive two-sided bounds for operator \ell_p to \ell_q norms of random
rectangular matrices with iid Weibull entries. We also discuss lower and upper bounds
for operator norms of other iid matrices. The talk is based on a joint work with Marta Strzelecka. -
Aldéric Joulin31/05/2023 14:45
In this talk, we will introduce the notion of intertwinings between (weighted) gradient and operators and see how those identities might be used to derive Poincaré type functional inequalities in various situations (non uniformly convex potentiels, perturbed product measures, log-concave measures on domains, etc.). This talk is based on a series of works in collaboration with Michel Bonnefont.
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Liran Rotem31/05/2023 16:10
It is well known that there are curious analogies between convex geometry and information theory. In particular, inequalities about entropy of random variables correspond to Brunn—Minkowski type inequalities about volumes of convex bodies.
In this talk we will discuss displacement concavity of entropy-like functionals, i.e. concavity with respect to geodesics in Wasserstein space. We will...
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Matthieu Fradelizi01/06/2023 09:45
I shall start by presenting an overview of some recent results on Fenchel and Bézout type inequalities on mixed volumes and Minkowski sums of convex bodies. In particular, there are better bounds in these inequalities in the case of zonoids. I shall also mention recent extensions to the Gaussian measures and other rotationally invariant measures.
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Based on work in common with Dylan Langharst,... -
Nathael Gozlan01/06/2023 11:10
In this talk, we will present new equivalent formulations of direct and converse Santalo inequalities involving the relative entropy functional
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and various optimal transport costs. We will explore this connection on various model probability spaces. We will see in particular that the Mahler conjecture for the volume product of convex bodies is equivalent to sharp bounds on the deficit in the... -
Mokshay Madiman01/06/2023 11:55
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Andrea Colesanti01/06/2023 14:00
After reviewing the log-Brunn-Minkowski inequality and its infinitesimal form, we will present some considerations about a possible functional form of this inequality. This will lead us to a functional inequality related to the standard Poincaré inequality for the Gaussian measure.
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Alexander Volberg01/06/2023 14:45
We consider a very high dimensional torus $\T^n$ and a rather sparse lattice of points on it. Then if an analytic polynomial of degree $d<<n$ is bounded on this lattice, then it is bounded on $\T^n$ independent of $n$. It is a joint project with Joe Slote and Haonan Zhang.
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Dario Cordero Erausquin01/06/2023 16:10
In proving inequalities for log-concave measures and convex bodies (often with the extra assumption of symmetry) one is lead to understand Poincaré type inequalities for all (symmetric) measure that are log-concave with respect to some given log-concave measure. When this reference measure is not Gaussian, this family does not belong to a classical $CD(\rho, \infinity)$ family. We will...
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Joseph Lehec01/06/2023 16:55
The talk will be mostly based on a joint work with Bo'az Klartag from last year in which we prove a polylog estimate for the Kannan, Lovasz, Simonovits (KLS) conjecture. If time permits I will also discuss more recent improvements of the bound.
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Pietro Caputo02/06/2023 09:45
We discuss some recent developments in the analysis of subadditivity and factorization properties of the relative entropy for spin systems on arbitrary graphs, and for uniformly random permutations. For spin systems these imply optimal modified log-Sobolev inequality for arbitrary block dynamics in the uniqueness region, including the case of non-local evolutions such as the Swendsen-Wang...
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Artem Zvavitch02/06/2023 11:10
The Busemann-Petty problem asks whether symmetric convex bodies in R^n with smaller (n−1)-dimensional volume of central hyperplane sections necessarily have smaller n-dimensional volume. The answer to this problem is affirmative for n less or equal to 4 and negative starting from dimension 5. Several extensions of this result have been shown in the case of measures on convex bodies, and...
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Max Fathi02/06/2023 11:55
In this talk, I will discuss a recent work of Sergey Bobkov on pointwise upper bounds for convolved probability density. In that work he shows a beautiful explicit estimate using the Cramer transform of the sum, which applies in particular to subgaussian random variables. If time allows, I will discuss some applications in the context of Stein's method and rates of convergence in the CLT,...
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