The Concentration of Measure Phenomenon

Research Project of the National Science Center

Welcome to the web page of the University of Warsaw Research Project "The Concentration of Measure Phenomenon" run under the National Science Center contract 2015/18/E/ST1/00214 in the years 2016-2021

Description of the project

The main objectives of the project is to explore several aspects of the theory of concentration of measure and its applications in high dimensional probability (in particular in Random Matrix Theory, Quantum Information Theory and in Markov Chain Monte Carlo Theory). The three main research areas of the project are

• Concentration of measure for non-Lipschitz functions
• Concentration of measure for convex functions
• Deviation inequalities for additive functionals of dependent sequences of random variables

A short description of the project is available at the National Science Center Site

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Participants

• Radosław Adamczak - Principal investigator
• Alan Czuroń - Postdoc
• Bartłomiej Polaczyk - PhD student

Former participants

• Michał Kotowski - Postdoc (October 2017 - September 2018)
• Michał Lemańczyk - PhD student (December 2016-November 2019)
• Bartłomiej Polaczyk - Master's student (December 2016 - November 2017)

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Publications

Beware: arXiv versions of the articles may (and usually do) differ from final journal versions.

• R. Adamczak, B. Polaczyk and M. Strzelecki, Modified log-Sobolev inequalities, Beckner inequalities and moment estimates (preprint) arXiv version
• J. Kułaga-Przymus, M. Lemańczyk, Hereditary subshifts whose measure of maximal entropy has no Gibbs property (preprint). arXiv version
• R. Adamczak, R. Latała, R. Meller, Moments of Gaussian chaoses in Banach spaces (preprint) arXiv version
• R. Adamczak, On almost sure convergence of random variables with finite chaos decomposition (preprint) arXiv version
• J. Björnberg, M. Kotowski, B. Lees, P. Miłoś, The interchange process with reversals on the complete graph, Electron. J. Probab. 24 (2019), no. 108, 1-43. arXiv version
• R. Adamczak, R. Latała, R. Meller, Hanson-Wright inequality in Banach spaces. To appear in Annales de l'Institut Henri Poincaré. arXiv version
• M. Lemańczyk, General Bernstein-like inequality for additive functionals of Markov chains . Journal of Theoretical Probability (2020). arXiv version
• B. Polaczyk, Concentration of the empirical spectral distribution of random matrices with dependent entries Electron. Commun. Probab. Volume 24 (2019), paper no. 78, 15 pp. arXiv version
• R. Adamczak, M. Kotowski, B. Polaczyk and M. Strzelecki, A note on concentration for polynomials in the Ising model. Electron. J. Probab. Volume 24 (2019), paper no. 42, 22 pp., arXiv version
• R. Adamczak, M. Kotowski and P. Miłoś, Phase transition for the interchange and quantum Heisenberg models on the Hamming graph. To appear in Annales de l'Institut Henri Poincaré. arXiv version
• R. Adamczak, Random non-Abelian G-circulant matrices. Spectrum of random convolution operators on large finite groups. To appear in Random Matrices: Theory and Applications arXiv version
• R. Adamczak, M. Strzelecki, On the convex Poincaré inequality and weak transportation inequalities. Bernoulli, Volume 25, Number 1 (2019), 341-374. arXiv version
• R. Adamczak, Metric and classical fidelity uncertainty relations for random unitary matrices, Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 10, arXiv version.

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