Combinatorics

On a girth-free variant of the Bourgain–Gamburd machine

I. Shkredov

Finite Fields and Their Applications 90, 102225 (2023)

A new connection between continued fractions and the Bourgain–Gamburd machine reveals a girth-free variant of this widely-celebrated theorem.

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Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"
Image for the paper "On a girth-free variant of the Bourgain–Gamburd machine"