BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giulio Tiozzo (Toronto)\, Sébastien Gouëzel (Rennes)\, Andrei Al peev (St-Petersburg) DTSTART:20210525T133000Z DTEND:20210525T163000Z DTSTAMP:20260710T044511Z UID:GroupTheoryENS/8 DESCRIPTION:Title: An afternoon on random walks and groups\nby Giulio Tiozzo (Toro nto)\, Sébastien Gouëzel (Rennes)\, Andrei Alpeev (St-Petersburg) as par t of ENS group theory seminar\n\n\nAbstract\n15.30 - 16.15 Giulio Tiozzo (Toronto)\n\n16.30 - 17.15 Sébastien Gouëzel (Rennes)\n\n17.45 - 18.30 Andrei Alpeev (St-Petersburg)\n\n\nGiulio Tiozzo\, "The fundamental ine quality for cocompact Fuchsian groups".\n\nA recurring question in the the ory of random walks on hyperbolic spaces asks whether the hitting (harmoni c) measures can coincide with measures of geometric origin\, such as the L ebesgue measure. This is also related to the inequality between entropy an d drift.\nFor finitely-supported random walks on cocompact Fuchsian groups with symmetric fundamental domain\, we prove that the hitting measure is singular with respect to Lebesgue measure\; moreover\, its Hausdorff dimen sion is strictly less than 1.\nAlong the way\, we prove a purely geometric inequality for geodesic lengths\, strongly reminiscent of the Anderson-Ca nary-Culler-Shalen inequality for free Kleinian groups.\nJoint with P. Kos enko.\n\n\nSébastien Gouëzel\, "Exponential estimates for random walks w ithout moment conditions on\nhyperbolic spaces"\n\nConsider a random walk on a nonelementary hyperbolic space (proper or not\, but one may just thi nk of a free group for simplicity). It is known\nthat the walk is convergi ng almost surely towards a point at a boundary\, and that the rate of esc ape is positive. We will discuss quantitative\nversions of these statement s: when can one show that these facts hold with an exponentially small pro bability for exceptions? While there are\nseveral such results in the lite rature\, the originality of our approach is that it does not require any m oment condition on the random walk. We\nwill discuss the main technical ne w idea in the case of the free group.\n\nAndrei Alpeev\, "Examples of dif ferent boundary behaviour of left and right random walks on groups".\n LOCATION:https://researchseminars.org/talk/GroupTheoryENS/8/ END:VEVENT END:VCALENDAR