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math.GT2022
Bottom of the Length Spectrum of Arithmetic Orbifolds
Mikolaj Fraczyk, Lam L. Pham
We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if the Salem numbers are uniformly bounded away from . We also prove an anal…
math.GR2022
Co-spectral radius of intersections
Mikolaj Fraczyk, Wouter van Limbeek
We study the behavior of the co-spectral radius of a subgroup of a discrete group under taking intersections. Our main result is that the co-spectral radius of an invariant…
math.PR2022
Co-spectral radius for countable equivalence relations
Miklós Abert, Mikolaj Fraczyk, Ben Hayes
We define the co-spectral radius of inclusions of discrete, probability measure-preserving equivalence relations, as the sampling exponent of a genera…