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math.GR2025
Uniform spectral gaps, non-abelian Littlewood-Offord and anti-concentration for random walks
Oren Becker, Emmanuel Breuillard
We show that random walks on semisimple algebraic groups do not concentrate on proper algebraic subvarieties with uniform exponential rate of anti-concentration. This is achieved b…
math.GR2025
Word maps and random words
Emmanuel Breuillard, Itay Glazer
We discuss some recent results by a number of authors regarding word maps on algebraic groups and finite simple groups, their mixing properties and the geometry of their fibers, em…