We present an intimate connection among the following fields:(a) distributed local
algorithms: coming from the area of computer science,(b) finitary factors of iid processes …

In this paper we consider coloring problems on graphs and other combinatorial structures on
standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings …

We show that every Borel graph $ G $ of subexponential growth has a Borel proper edge-
coloring with $\Delta (G)+ 1$ colors. We deduce this from a stronger result, namely that an …

Asymptotic separation index is a parameter that measures how easily a Borel graph can be
approximated by its subgraphs with finite components. In contrast to the more classical …

We study graphs of polynomial growth from the perspective of asymptotic geometry and
descriptive set theory. The starting point of our investigation is a theorem of Krauthgamer …

This text provides an introduction to the field of distributed local algorithms--an area at the
intersection of theoretical computer science and discrete mathematics. We collect many …

The Lov\'asz Local Lemma (the LLL for short) is a powerful tool in probabilistic combinatorics
that is used to verify the existence of combinatorial objects with desirable properties. Recent …

In the past couple of years a rich connection has been found between the fields of
descriptive set theory and distributed computing. Frequently, and less surprisingly, finitary …

Let $\Gamma $ be a countably infinite group. Given $ k\in\mathbb {N} $, we use $\mathrm
{Free}(k^\Gamma) $ to denote the free part of the Bernoulli shift action of $\Gamma $ on …