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We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy power inequalities… (More)

- Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
- ArXiv
- 2018

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian… (More)

- Maciek D. Korzec, Piotr Nayar, Piotr Rybka
- SIAM J. Math. Analysis
- 2012

In this paper we study a sixth order Cahn-Hilliard type equation that arises as a model for the faceting of a growing surface. We show global in time existence of weak solutions and uniform in time a… (More)

- Piotr Nayar, Tomasz Tkocz
- 2014

In this note we consider a certain class of convolution operators acting on the Lp spaces of the one dimensional torus. We prove that the identity minus such an operator is nicely invertible on the… (More)

- Piotr Nayar, Tomasz Tkocz
- 2013

We give counterexamples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

We derive Khinchine type inequalities for even moments with optimal constants from the result of Walkup (J Appl Probab 13:76–85, 1976) which states that the class of log-concave sequences is closed… (More)

- Piotr Nayar, Tomasz Tkocz
- 2017

We prove a dimension-free tail comparison between the Euclidean norms of sums of independent random vectors uniformly distributed in centred Euclidean spheres and properly rescaled standard Gaussian… (More)

- Piotr Nayar
- 2009

It is known that many high-dimensional probability distributions μ on the Euclidean space R n (and other metric spaces, including graphs) possess strong concentration properties. In a functional… (More)

Our goal is to write an extended version of the notes of a course given by Olivier Guédon at the Polish Academy of Sciences from April 11-15, 2011. The course is devoted to the study of concentration… (More)