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Krzysztof Oleszkiewicz

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Moments of the Distance Between Independent Random VectorsConcentration of Measure Phenomena2020-10-19
Proves quantitative reversals of the triangle-integral bound for independent Banach-space-valued vectors and identifies optimal constants: constant 3 for p=1…
Talk
On Mimicking Rademacher SumsFunctional Inequalities in Discrete Spaces with Applications 20132013-09-30
For the discrete cube with fixed cutoff K the L1 distance from the Rademacher sum to the subspace of only high frequencies is Θ(K): an explicit function is…
Talk
Introduction to Analysis on the Discrete Cube IReal Analysis Boot Camp 20132013-09-09
Defines the discrete cube {-1,1}^n with normalized counting measure, L^p norms and Hamming distance, then builds the Walsh functions as an orthonormal basis of…
Talk
Introduction to Analysis on the Discrete Cube IIReal Analysis Boot Camp 20132013-09-09
Shows that two constructions of the continuous-time random walk on the discrete cube — the lazy discrete-time walk rescaled and independent coordinate Poisson…
Talk
Introduction to Analysis on the Discrete Cube IIIReal Analysis Boot Camp 20132013-09-09
Compares concrete semigroups and computes generators explicitly: shift group has generator −d/dx and fails analytic recovery for smooth nonanalytic examples…
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Introduction to Analysis on the Discrete Cube IVReal Analysis Boot Camp 20132013-09-09
Shows the discrete-cube log‑Sobolev inequality holds with constant 2 and derives hypercontractivity bounds that recover Bonami/Kahane moment comparisons for…
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