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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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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.
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Oct. 31, 2024, 12:15 p.m.
Witold Bednorz (Uniwersytet Warszawski)
Some consequences of the new approach to positive stochastic processes. (Some consequences of the new approach to positive stochastic processes.)
In my talk I will explain our idea of an equivalent characterization of the supremum expectation of positive stochastic processes. Some consequences will be discussed, in particular for the Sudakov minoration for canonical processes based …
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Oct. 17, 2024, 12:15 p.m.
Rafał Latała (Uniwersytet Warszawski)
Operator \ell_p to \ell_q norms of structured Gaussian matrices (Operator \ell_p to \ell_q norms of structured Gaussian matrices)
We discuss two-sided bounds for operator \ell_p to \ell_q norms of structured Gaussian matrices in the case 1\le p\le 2\le q\leq \infty. Guédon, Hinrichs, Litvak and Prochno conjectured that an easy lower bound for the …
