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September 2021 On convergence of random walks on moduli space
Roland Prohaska
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Illinois J. Math. 65(3): 735-747 (September 2021). DOI: 10.1215/00192082-9421088

Abstract

The purpose of this paper is to establish convergence of random walks on the moduli space of abelian differentials on compact Riemann surfaces in two different modes: convergence of the n-step distributions from almost every starting point in an affine invariant submanifold toward the associated affine invariant measure, and almost sure pathwise equidistribution toward the affine invariant measure on the SL2(R)-orbit closure of an arbitrary starting point. These are analogues to previous results for random walks on homogeneous spaces.

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Roland Prohaska. "On convergence of random walks on moduli space." Illinois J. Math. 65 (3) 735 - 747, September 2021. https://doi.org/10.1215/00192082-9421088

Information

Received: 9 February 2021; Revised: 24 June 2021; Published: September 2021
First available in Project Euclid: 3 August 2021

Digital Object Identifier: 10.1215/00192082-9421088

Subjects:
Primary: 60B15
Secondary: 22F10, 32G15, 60G50

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 3 • September 2021
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