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Cotygodniowe seminarium badawcze.
2023-11-30, godz. 12:15, 3160
Michał Kotowski (Uniwersytet Warszawski)
The local and global limit of the continuous-time Mallows process
The Mallows process is a process of random permutations whose marginal at time $t$ is the Mallows distribution with parameter $t$. It can be thought of as interpolating between the identity permutation and the reverse permutation on $n$ elements. We prove that under an appropriate space and time ...
2023-11-23, godz. 12:15, 3160
Witold Bednorz (Uniwersytet Warszawski)
Recently, the Talagrand conjecture regarding selector processes has been proved: work by Pham and Park. This conjecture concerned the characterization of the expected value of the process supremum in terms of the existence of an appropriate small coverage of a random event describing the process sup...
2023-11-16, godz. 12:15, 3160
Adam Osękowski (Uniwersytet Warszawski)
Paraprodukty to operatory pojawiające się w naturalny sposób w teorii całek singularnych; z grubsza rzecz ujmując, dowolny operator singularny daje się rozłożyć na sumę dwóch paraproduktów oraz zwykłego operatora splotowego. Z uwagi na ten fakt, pojawia się naturalne ...
2023-11-09, godz. 12:15, 3160
Marcin Kotowski (CFT PAN)
Circuit complexity of unitary evolutions generated by random GUE Hamiltonians
I will present some applications of random matrix theory and concentration of measure on the unitary group to the problem of circuit complexity in quantum computing. Quantum time evolutions are described by unitary matrices. Circuit complexity of a unitary matrix is the minimal number of "eleme...
2023-10-26, godz. 12:15, 3160
Rafał Martynek (Uniwersytet Warszawski)
Lipschitz comparison for Bernoulli processes
I’ll discuss an improvement of the recent result by Chu and Raginsky (https://arxiv.org/pdf/2304.14474.pdf) concerning comparison of the expected suprema of Bernoulli processes with respect to some Lipschitz mapping. Our result (together with Witold Bednorz) is based on constructing appropr...
2023-10-12, godz. 12:15, 3160
Maciej Wiśniewolski
During my talk i will show some new representations of Laplace transforms of the Gaussian Multiplicative Chaos (GMC) on Euclidean balls in R^d. I will discuss the problem of small deviations of GMC and their lognormal asymptotic bounds. I will also present some ideas how to use GMC in the problem ...
2023-10-05, godz. 12:15, 3160
Kunal Dutta (Uniwersytet Warszawski)
Dimensionality Reduction for Persistent Homology with Gaussian Kernels
Computing persistent homology using Gaussian kernels is useful in the domains of topological data analysis and machine learning. We consider a power distance version of the Gaussian kernel distance (GKPD) given by Phillips, Wang and Zheng, and show that for high-dimensional datasets, the persistent ...
2023-05-25, godz. 12:15, 3160
Rafał Latała (Uniwersytet Warszawski)
We will present a Chevet-type inequality for subexpontial Weibull processes and show how it may be applied to find two-sided bounds for operator \ell_p to \ell_q norms of random rectangular matrices with iid Weibull entries. We will also discuss lower and upper bounds for operator norms of other iid...
2023-05-18, godz. 12:15, 5820 (please note the change of room)
Alexandros Eskenazis (Sorbonne Université)
Discrete logarithmic Sobolev inequalities in Banach spaces
We shall discuss certain aspects of vector-valued harmonic analysis on the discrete hypercube. After presenting the geometric motivation behind such investigations, we will survey known results on the Poincaré inequality and Talagrand’s influence inequality. Then we will proceed to pres...
2023-05-11, godz. 12:15, 3160
Dominik Kutek (Uniwersytet Warszawski)
On Orlicz spaces satisfying the Hoffmann-Jørgensen inequality
We say that an Orlicz function \Psi satisfies the H-J inequality, if \| \sum_{k=1}^n X_k \|_{\Psi} \le C_{\Psi} ( \| \sum_{k=1}^n X_k \|_{L_1} + \| \max_{k \le n}\|X_k\| \|_{\Psi}) for any collection \{X_k\}_{k \le n} of zero mean and independent random variables taking values in any separable Banac...
