Strong uniform expansion in $\mathrm{SL}(2,p)$

Emmanuel Breuillard, Alex Gamburd

We show that there is an infinite set of primes $\mathcal{P}$ of density one, such that the family of \textit{all} Cayley graphs of $\mathrm{SL}(2,p)$%, $p\in \mathcal{P}$, is a fa…