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arXiv · 2412.11571

Borel Local Lemma: arbitrary random variables and limited exponential growth

Anton Bernshteyn·Jing Yu
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Abstract

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. Recent years saw the development of various "constructive" versions of the LLL. A major success of this research direction is the Borel version of the LLL due to Csóka, Grabowski, Máthé, Pikhurko, and Tyros, which holds under a subexponential growth assumption. A drawback of their approach is that it only applies when the underlying random variables take values in a finite set. We present an alternative proof of a Borel version of the LLL that holds even if the underlying random variables are continuous and applies to dependency graphs of limited exponential growth.

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Anton Bernshteyn, Jing Yu. 2026-05-27. Borel Local Lemma: arbitrary random variables and limited exponential growth. https://arxiv.org/abs/2412.11571

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