Weekly research seminar
Organizers
- prof. dr hab. Rafał Latała
Information
Thursdays, 12:15 p.m. , room: 3160Home page
http://lists.mimuw.edu.pl/listinfo/sem-rpList of talks
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May 22, 2025, 12:15 p.m.
Lorenzo Sadun (University of Texas at Austin)
Random graphs with near-extreme triangle counts
We consider large dense random graphs with constraints on the densities $(e,t)$ of edges and triangles. For values of $(e,t)$ near the boundary of the ``Razborov triangle'', we show that all but an exponentially small …
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May 15, 2025, 12:15 p.m.
Ioannis Kavvadias (University of Warsaw)
Follmer process: Functional Inequalities and Concentration for Convex functions (Follmer process: Functional Inequalities and Concentration for Convex functions)
We will prove a representation formula for Gaussian relative entropy given by J. Lehec and use it to prove several functional inequalities. Moreover, we give a representation formula for the log-Laplace transform via stochastic processes …
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April 10, 2025, 12:15 p.m.
Adam Osękowski (Uniwersytet Warszawski)
Inequalities for a nonnegative submartingale and the nondecreasing component coming from the Doob-Meyer decomposition (Nierówności dla nieujemnego podmartyngału i składowej niemalejącej z rozkładu Dooba-Meyera)
An arbitrary nonnegative submartingale can be expressed as the sum M+A, where M is a local martingale starting from zero and A is a non-decreasing process. During the talk we will discuss the sharp comparison …
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April 3, 2025, 12:15 p.m.
Rafał Latała (University of Warsaw)
Upper bound on the injective norm of sums of Gaussian random tensors via the PAC Bayesian lemma (after I.Aden-Ali) (Upper bound on the injective norm of sums of Gaussian random tensors via the PAC Bayesian lemma (after I.Aden-Ali))
We will discuss a recent result of Ishaq Aden-Ali (On the Injective Norm of Sums of Random Tensors and the Moments of Gaussian Chaoses, arXiv:2503.10580) and show how the PAC-Bayesian lemma (a simple consequence of …
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March 27, 2025, 12:15 p.m.
Maud Szusterman (Uniwersytet Warszawski)
Revisiting Banaszczyk's 5K-theorem (Revisiting Banaszczyk's 5K-theorem)
Banaszczyk's 5K-theorem is an important result in combinatorics. It states that in any dimension n, given any finite sequences of vectors u_1, ... , u_t taken from the unit ball B_2^n , and given any …
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March 20, 2025, 12:15 p.m.
Jacek Jakimiuk
Stability of Khintchine inequalities with optimal constants (Stability of Khintchine inequalities with optimal constants)
We give a strengthening of the classical Khintchine inequality between the second and the $p$-th moment for $p \ge 3$ with optimal constant by adding a deficit depending on the vector of coefficients of the …
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March 6, 2025, 12:15 p.m.
Eli Putterman (Tel Aviv University)
Small-ball probabilities for mean widths of random polytopes (Small-ball probabilities for mean widths of random polytopes)
The classical theory of random polytopes addresses questions such as computing the expectation or variance of geometric parameters associated to a random polytope (e.g., volume, number of facets, or mean width); more recent theory also …
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Feb. 27, 2025, 12:15 p.m.
Marta Strzelecka (University of Warsaw)
Operator \ell_p to \ell_q norms of structured Gaussian matrices (Operator \ell_p to \ell_q norms of structured Gaussian matrices)
We report the progress in two-sided bounds for operator norms from \ell_p to \ell_q of structured Gaussian matrices in the case when p^*,q>=2. Guédon, Hinrichs, Litvak and Prochno conjectured that in this range an easy …
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Jan. 16, 2025, 12:15 p.m.
Adam Osękowski (Uniwersytet Warszawski)
Two-weight inequalities for certain dyadic operators (Nierówności dwuwagowe dla pewnych diadycznych operatorów)
We will be interested in a certain special class of martingale operators, which can be regarded as discrete analogues of classical operators of harmonic analysis: singular integrals and Riesz potentials. We will provide the characterization …
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Dec. 19, 2024, 12:15 p.m.
Daniel Murawski (Uniwersytet Warszawski)
Optimal constants C_{p, 4} in Khintchine inequality (Optimal constants C_{p, 4} in Khintchine inequality)
We prove that whenever S is a weighted sum of n independent Rademacher random variables, then ||S||_p / ||S||_4 \leq ||G||_p / ||G||_4, where G is a standard Gaussian random variable and p \geq 4. …
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Dec. 12, 2024, 12:15 p.m.
Michał Strzelecki (Uniwersytet Warszawski)
Lower bounds for weak-type constants of some operators (Lower bounds for weak-type constants of some operators)
In the talk I shall present a counterexample to a conjecture of Gill about the exact value of the weak-type (1,1) constant of some Hardy-type operators (which arise when one restricts the Beurling-Ahlfors transform to …
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Nov. 28, 2024, 12:15 p.m.
Maciej Rzeszut
Gaussian approximation of B-splines in Schwartz seminorms (Gaussian approximation of B-splines in Schwartz seminorms)
We consider sections of the $n-1$ dimensional simplex $\Delta_{n-1}= \left\{y\in\R_+^n: \sum_k y_k= 1\right\}$ by hyperplanes $\sum x_k y_k=t$, for a vector $x$ satisfying the assumptions of Berry-Esseen theorem, i.e. $\sum x_k=0,\sum x_k^2=1$ and $m^3:=\sum\left|x_k\right|^3$ is …
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Nov. 21, 2024, 12:15 p.m.
Dominik Kutek (University of Warsaw)
Bregman variation of semimartingales (Bregman variation of semimartingales)
The quadratic variation is a key concept in stochastic calculus, with widespread applications in mathematics and economy. The talk will be about a similar, but more general concept, the Bregman variation (or phi-variation) of semimartingales. …
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Nov. 14, 2024, 12:15 p.m.
Peter Pivovarov (Univeristy of Missouri)
Stochastic methods in dual Brunn--Minkowski theory (Stochastic methods in dual Brunn--Minkowski theory)
The surface area of a convex body can be obtained as an average of the areas of its shadows (1-codimensional projections). In turn, the surface area is just one of the k-quermassintegrals of a convex …
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Nov. 7, 2024, 12:15 p.m.
Tomasz Tkocz
Convexity properties of sections and Rademacher sums (Convexity properties of sections and Rademacher sums)
I shall discuss certain convexity properties of hyperplane sections of 1-symmetric convex bodies as well as Rademacher sums, which are motivated by chessboard cutting problems and the logarithmic Brunn-Minkowski problem.