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
  • Michał Lemańczyk - PhD student
  • Bartłomiej Polaczyk - PhD student

Former participants

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

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Publications

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

  • J. Björnberg, M. Kotowski, B. Lees, P. Miłoś, The interchange process with reversals on the complete graph, arXiv version
  • R. Adamczak, R. Latała, R. Meller, Hanson-Wright inequality in Banach spaces, arXiv version
  • M. Lemańczyk, General Bernstein-like inequality for additive functionals of Markov chains arXiv version
  • B. Polaczyk, Concentration of the empirical spectral distribution of random matrices with dependent entries arXiv version
  • R. Adamczak, M. Kotowski, B. Polaczyk and M. Strzelecki, A note on concentration for polynomials in the Ising model arXiv version
  • R. Adamczak, M. Kotowski and P. Miłoś, Phase transition for the interchange and quantum Heisenberg models on the Hamming graph (preprint). arXiv version
  • R. Adamczak, Random non-Abelian G-circulant matrices. Spectrum of random convolution operators on large finite groups (preprint). arXiv version
  • R. Adamczak, M. Strzelecki, On the convex Poincaré inequality and weak concentration inequalities, accepted for Bernoulli, 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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Working seminar - selected Wednesdays, 10:15-11:45, Banacha 2 (Faculty of Mathematics, Informatics and Mechanics), room 2270

  • December 19, 2018 - M. Strzelecki - On A Mixture Of Brenier and Strassen Theorems (after Gozlan, Juillet) - continuation
  • December 6, 2018 - M. Strzelecki - On A Mixture Of Brenier and Strassen Theorems (after Gozlan, Juillet)
  • November 27, 2018 - B. Polaczyk - Concentration of measure for random fields (after Chazottes, Redig) - continuation
  • October 24, 2018 - B. Polaczyk - Concentration of measure for random fields (after Chazottes, Redig)
  • October 18, 2018 - (within the Probability Group Seminar) B. Polaczyk - Concentration for polynomials in the Ising model
  • October 10, 2018 - M. Lemańczyk - Weighted sampling without replacement (after Ben Hamou, Peres, Salez) - continuation
  • October 10, 2018 - M. Lemańczyk - Weighted sampling without replacement (after Ben Hamou, Peres, Salez)
  • April 18, 2018 - Michał Kotowski - Approximate tensorization of entropy (after Marton)
  • April 11, 2018 - Michał Kotowski - Concentration for polynomials of the Ising model (after Goetze, Sambale, Sinulis and Gheissari, Lubetzky, Peres)
  • April 5, 2018 - (within the Probability Group Seminar) R. Adamczak - Spectrum of random non-Abelian G-circulants
  • April 4, 2018 - B. Polaczyk - Higher order concentration inequalities for weakly dependent random variables (after Goetze, Sambale, Sinulis)
  • March 7, 2018 - M. Kotowski - Concentration of measure for cycle statistics of uniform random permutations (after Manstavicius)
  • December 20, 2017 - M. Lemańczyk - Lieb's inequality and tail bounds for sums of independent random matrices (after Tropp)
  • October 19, 2017 - (within the Probability Group Seminar) M. Strzelecki - Inequalities for convex functions and Talagrand's conjecture (after Gozlan, Madiman, Roberto, Samson)
  • October 18, 2017 - B. Polaczyk - Brenier's theorem
  • October 11, 2017 - B. Polaczyk - The Benamou-Brenier formula
  • June 8, 2017 - (within the Probability Group Seminar) M. Lemańczyk, Bernstein type inequality for one-dependent variables and Markov chains
  • April 27, 2017 (within the Probability Group Seminar) - R. Adamczak - The convex Poincaré inequality and weak transportation inequalities (based on joint work with M. Strzelecki)
  • April 24, 2017 - M. Lemańczyk - Bounded difference inequalities for Markov chains (after Dedecker-Gouëzel)
  • March 27, 2017 - B. Polaczyk - Concentration inequalities for random matrices - continuation
  • March 13, 2017 - B. Polaczyk - Concentration inequalities for random matrices (after Guionnet-Zeitouni)
  • March 6, 2017 - M. Strzelecki: Characterization of convex log-Sobolev inequalities on the line - continuation
  • February 27, 2017 - M. Strzelecki: Characterization of convex log-Sobolev inequalities on the line (based on joint work with Yan Shu)
  • January 16, 2017 - R. Adamczak: Kantorovich duality
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Positions

A 12-month postdoc position. Deadline for applications - April 14, 2018. Details can be found here

(Closed) A two-year PhD position. Details (in Polish) can be found here

(Closed) A three-year PhD position. Details (in Polish) can be found here. Please contact the PI directly if you need the details in English.

(Closed) A one-year postoc position. Deadline for applications on April 30, 2017. Click here for details

Last edited on Oct 11, 2018

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