On the spectral gap conjecture for pairs in SU(2)

Oleg Pikhurko, Kohki Sakamoto

For $n\ge 2$, Gamburd, Jakobson, and Sarnak [J. Eur. Math. Soc. 1, 51-85 (1999)] conjectured that almost every $n$-tuple in $\mathrm{SU}(2)$ has a spectral gap. Toward this conjec…