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math.CO2024
Borel Local Lemma: arbitrary random variables and limited exponential growth
Anton Bernshteyn, Jing Yu
The Lovász 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…
math.CO2024
Embedding Borel graphs into grids of asymptotically optimal dimension
Anton Bernshteyn, Jing Yu
Let be a Borel graph all of whose finite subgraphs embed into the -dimensional grid with diagonals. We show that then itself admits a Borel embedding into the Schreier g…