BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ilya Gekhtman (Technion) DTSTART:20210308T143000Z DTEND:20210308T154500Z DTSTAMP:20260423T021424Z UID:BODS/13 DESCRIPTION:Title: Gi bbs measures vs. random walks in negative curvature\nby Ilya Gekhtman (Technion) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nThe id eal boundary of a negatively curved manifold naturally\ncarries two types of measures.\nOn the one hand\, we have conditionals for equilibrium (Gibb s) states\nassociated to Hoelder potentials\; these include the Patterson- Sullivan\nmeasure and the Liouville measure. On the other hand\, we have s tationary\nmeasures coming from random walks on the fundamental group.\n We compare and contrast these two classes.First\, we show that both\nof t hese of these measures can be associated to geodesic flow invariant\nmeasu res on the unit tangent bundle\, with respect to which closed\ngeodesics s atisfy different equidistribution properties. Second\, we show\nthat the a bsolute continuity between a harmonic measure and a Gibbs\nmeasure is equi valent to a relation between entropy\, (generalized)\ndrift and critical exponent\, generalizing previous formulas of\nGuivarc’h\, Ledrappier\, a nd Blachere-Haissinsky-Mathieu. This shows that\nif the manifold (or more generally\, a CAT(-1) quotient) is geometrically\nfinite but not convex co compact\, stationary measures are always singular\nwith respect to Gibbs m easures.\nA major technical tool is a generalization of a deviation inequa lity due\nto Ancona saying the so called Green distance associated to the random\nwalk is nearly additive along geodesics in the universal cover.\nP art of this is based on joint work with Gerasimov-Potyagailo-Yang and\npar t on joint work with Tiozzo.\n LOCATION:https://researchseminars.org/talk/BODS/13/ END:VEVENT END:VCALENDAR