On a girth-free variant of the Bourgain-Gamburd machine
Ilya D. Shkredov
TL;DR
This paper introduces a girth-free variant of the Bourgain-Gamburd machine and explores its applications across additive combinatorics, number theory, and probability, broadening the machine's utility.
Contribution
The paper presents a new version of the Bourgain-Gamburd machine that does not rely on girth bounds, expanding its applicability.
Findings
Developed a girth-free Bourgain-Gamburd machine variant
Applied the new machine to problems in additive combinatorics
Extended the machine's use to number theory and probability
Abstract
A variant of the Bourgain-Gamburd machine without using any girth bounds is obtained. Also, we find series of applications of %our result the Bourgain-Gamburd machine to problems of Additive Combinatorics, Number Theory and Probability.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Cellular Automata and Applications · semigroups and automata theory