---
title: '18.156 notes 19: random walks on finite groups iii'
description: We discuss how projection theory appears in the work of Bourgain-Gamburd.
date: '2025-04-24'
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created: '2025-04-24'
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published: '2025-04-24'
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We discuss how projection theory appears in the work of Bourgain-Gamburd. Builds on work of Helfgott, Hrushovski, and Larsen-Pink.

We did not make notes for this lecture. A detailed reference is in Tao’s class notes <https://terrytao.wordpress.com/2012/01/13/254b-notes-4-the-bourgain-gamburd-expansion-machine/> and <https://terrytao.wordpress.com/2012/02/05/254b-notes-5-product-theorems-pivot-arguments-and-the-larsen-pink-non-concentration-inequality/>