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The ubiquity of optimal spectral gaps

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A random cover of a compact hyperbolic surface has relative spectral gap 3/16−ε.

Author(s): Magee, M., Naud, F. & Puder, D.
Published in: Geometric and Functional Analysis, 2022, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-022-00602-x

Random Unitary Representations of Surface Groups I: Asymptotic expansions

Author(s): Michael Magee
Published in: Communications in Mathematical Physics, 2022, Vol.391(1), pp.119-171 [Peer Reviewed Journal], 1, 2022, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04295-5