BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joonas Turunen (Laboratoire de physique\, ENS de Lyon) DTSTART:20220613T090000Z DTEND:20220613T100000Z DTSTAMP:20260423T024424Z UID:IPHT-PHM/4 DESCRIPTION:Title: Statistical mechanics models on random lattices of the half-plane\nby Joonas Turunen (Laboratoire de physique\, ENS de Lyon) as part of Sémina ire de physique mathématique IPhT\n\nLecture held in Salle Claude Itzykso n\, Bât. 774\, Orme des Merisiers.\n\nAbstract\nIn the main part of the t alk\, which is mostly based on joint works with Linxiao Chen\, we start fr om a purely combinatorial problem of random planar triangulations of the d isk coupled with an Ising model (either on the faces or the on the vertice s) with Dobrushin boundary conditions and at a fixed temperature. We ident ify rigorously a phase transition by analysing the critical behaviour of t he partition functions of a large disk at and around the critical point. M oreover\, we study the random geometric implications of this in particular in the local limit when the disk perimeter tends to infinity. At the crit ical temperature\, we also find some explicit scaling limits of observable s related to the interface lengths as well as scaling limits of perimeter fluctuations associated with a Markovian exploration process of the half-p lane Ising triangulation. The two key techniques in use are singularity an alysis of rational parametrizations of generating functions\, as well as t he aforementioned exploration process. In the remaining part (time permitt ing)\, I will explain more informally our ongoing project with Jérémie B outtier and Grégory Miermont about how the above approach could be genera lized to study random planar maps of a disk decorated with O(n) loop model s (where rational parametrizations do not necessarily exist).\n LOCATION:https://researchseminars.org/talk/IPHT-PHM/4/ END:VEVENT END:VCALENDAR