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 …

Consider any locally checkable labeling problem Π in rooted regular trees: there is a finite
set of labels Σ, and for each label χ x Σ we specify what are permitted label combinations of …

We consider the algorithmic problem of finding large balanced independent sets in sparse
random bipartite graphs, and more generally the problem of finding independent sets with …

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 …

We study the local complexity landscape of locally checkable labeling (LCL) problems on
constant-degree graphs with a focus on complexities below log* n. Our contribution is …

Let $(X,\tau) $ be a Polish space with Borel probability measure $\mu $, and $ G $ a locally
finite one-ended Borel graph on $ X $. We show that $ G $ admits a Borel one-ended …

We give practical, efficient algorithms that automatically determine the asymptotic distributed
round complexity of a given locally checkable graph problem in the $[\Theta (\log n),\Theta …

We introduce new types of examples of bounded degree acyclic Borel graphs and study
their combinatorial properties in the context of descriptive combinatorics, using a …

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 …

The locality of a graph problem is the smallest distance T such that each node can choose
its own part of the solution based on its radius-T neighborhood. In many settings, a graph …