Piotr Nayar

Global weak solutions to a sixth order Cahn-Hilliard type equation

We study a sixth order Cahn--Hilliard type equation that arises as a model for the faceting of a growing surface. We show existence of global-in-time weak solutions in two space dimensions, assuming periodic boundary conditions. We also establish exponential-in-time a priori estimates on the

A note on a Brunn-Minkowski inequality for the Gaussian measure

H^3

A note on the convex infimum convolution inequality

norm of solutions. These bounds enable us to prove the uniqueness of weak solutions. We also show the regularizing effect of the equation on the data.

Gaussian mixtures: Entropy and geometric inequalities

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

Concentration Properties of Restricted Measures with Applications to Non-Lipschitz Functions

We characterize the symmetric measures which satisfy the one dimensional convex infimum convolution inequality of Maurey. For these measures the tensorization argument yields the two level Talagrands concentration inequalities for their products and convex sets in

Two-sided bounds for Lp-norms of combinations of products of independent random variables

\mathbb{R}^n

On a Loomis–Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies

.

A note on certain convolution operators

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 random variable. Examples of Gaussian mixtures include random variables with densities proportional to

A reverse entropy power inequality for log-concave random vectors

e^{-|t|^p}

Concentration inequalities and geometry of convex bodies

and symmetric