Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …

In this article, we study the excursion sets 𝒟 p= f-1 ([-p,+∞[) where f is a natural real-analytic
planar Gaussian field called the Bargmann–Fock field. More precisely, f is the centered …

Most correlation inequalities for high-dimensional functions in the literature, such as the
Fortuin-Kasteleyn-Ginibre (FKG) inequality and the celebrated Gaussian Correlation …

In the present paper, we use the semigroup method to investigate various functional
inequalities invoking L 1 and L p norms in the framework of canonical anti-commuting …

This lecture studies the analysis of Boolean functions and present a few ideas, results,
proofs, and problems. We start with the wider picture of expansion in graphs and then …

We discuss a general method to prove quantitative improvements on correlation inequalities
and apply it to arm estimates for Bernoulli bond percolation on the square lattice. Our first …

Let F⊂ 2 [n] be a family in which any three sets have non-empty intersection and any two
sets have at least 32 elements in common. The nearly best possible bound F≤ 2 n− 2 is …

Chvátal's conjecture in extremal combinatorics asserts that for any decreasing family F of
subsets of a finite set S, there is a largest intersecting subfamily of F consisting of all …

For a function f over the discrete cube, the total L1 influence of f is defined as the sum of the
L1 norm of the discrete derivatives of f in all n directions. In this work, we show that in the …

Many correlation inequalities for high-dimensional functions in the literature, such as the
Harris–Kleitman inequality, the Fortuin–Kasteleyn–Ginibre inequality and the celebrated …