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A zero–one law for the spectral gap property of pairs in SU(2)
Oleg Pikhurko, Kohki Sakamoto
Source abstract
Abstract For , Gamburd, Jakobson, and Sarnak [ J. Eur. Math. Soc . 1 (1999), 51–85] conjectured that almost every ‐tuple in has a spectral gap. Toward this conjecture, Fisher [ Int. Math. Res. Not . (2006), Art. ID 26028] established a zero–one law for , but obtained only a partial result for . In this paper, we prove that the zero–one law also holds for . We also remark that a Baire categorical analogue of this result holds.
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