Many mathematical models of statistical physics in two dimensions are either known or
conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions …

Percolation models describe the inside of a porous material. The theory emerged timidly in
the middle of the twentieth century before becoming one of the major objects of interest in …

It is shown that a large class of events in a product probability space are highly sensitive to
noise, in the sense that with high probability, the configuration with an arbitrary small percent …

The enormous amount of data produced by mobile and IoT devices has motivated the
development of federated learning (FL), a framework allowing such devices (or clients) to …

We consider a wireless sensor network, where nodes switch between an active (on) and a
slee** (off) mode, to save energy. The basic assumptions are that the on/off schedules are …

This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying
on the border of probability theory, discrete mathematics, analysis, and theoretical computer …

Preface 2. Basic Definitions and a Few Highlights 3. Galton-Watson Trees 4. General
percolation on a connected graph 5. The First-Moment Method 6. Quasi-independent …

One goal of this paper is to prove that dynamical critical site percolation on the planer
triangular lattice has exceptional times at which percolation occurs. In doing so, new …

This work is the first in a series of papers devoted to the construction and study of scaling
limits of dynamical and near-critical planar percolation and related objects like invasion …

Consider the indicator function f of a 2-dimensional percolation crossing event. In this paper,
the Fourier transform of f is studied and sharp bounds are obtained for its lower tail in …