Random walks on punctured convex real projective surfaces

Abstract: I'll discuss the following result, joint with Giulio Tiozzo: Letting $\Gamma$ be the representation of a punctured hyperbolic surface group in $PSL(3,R)$ acting discretely, properly discontinuously, and with finite co-volume on a properly convex set in the projective plane, we have that hitting measure for a random walk on any $\Gamma$-orbit with certain moment conditions is singular with respect to the classical Patterson-Sullivan measure. The approach extends and adapts the strategy of Maher-Tiozzo for punctured hyperbolic surfaces. We also prove an essential global shadow lemma for finite volume convex real projective manifolds.

differential geometrygeometric topology

Audience: researchers in the topic

Columbia geometric topology seminar

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