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.

This talk is hosted by Columbia University. Link to the talk site.