EVENT DETAILS AND ABSTRACT

Title: Gibbs measures for CAT(-1) spaces - a geometric approach that survives branching
Speaker: Daniel Thompson
Speaker Info: Ohio State
Brief Description:
Special Note:
Abstract:

Consider a general CAT(-1) space and a bounded H\”older potential on the space of geodesics. We describe how to construct a Gibbs measure using appropriate weighted “quasi”-Patterson densities. If the Gibbs measure is finite, then it is an ergodic equilibrium state. We thus generalize results of Paulin, Pollicott, Schapira (for pinched negative curvature manifolds) and Roblin (for the 0-potential for CAT(-1) spaces). Unlike previous results in this direction in the CAT(-1) setting, our construction does not require a condition that the potential must agree over geodesics that share a common segment, which is a restrictive condition beyond the Riemannian case. The branching phenomenon is typical in CAT(-1) spaces and has been a major obstacle to fully developing the theory of equilibrium states in this setting - to fully allow branching, much of our construction takes a “quasi” approach which allows “wiggle” by appropriate constants. This is joint work with Caleb Dilsavor (Ohio State).