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Lengths of closed geodesics on random surfaces of large genus (1710.09727v2)
Published 26 Oct 2017 in math.GT and math.PR
Abstract: We prove Poisson approximation results for the bottom part of the length spectrum of a random closed hyperbolic surface of large genus. Here, a random hyperbolic surface is a surface picked at random using the Weil-Petersson volume form on the corresponding moduli space. As an application of our result, we compute the large genus limit of the expected systole.
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