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arXiv · 2102.04083

On Convergence of Random Walks on Moduli Space

Roland Prohaska
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Abstract

The purpose of this note 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 towards the associated affine invariant measure, and almost sure pathwise equidistribution towards the affine invariant measure on the $SL_2(\mathbb{R})$-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. 2021-06-22. On Convergence of Random Walks on Moduli Space. https://doi.org/10.1215/00192082-9421088

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