BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Valentin Féray (IECL\, CNRS et Université de Lorraine) DTSTART:20230403T090000Z DTEND:20230403T100000Z DTSTAMP:20260423T024355Z UID:IPHT-PHM/21 DESCRIPTION:Title: Components of meandric systems and the infinite noodle\nby Valentin Féray (IECL\, CNRS et Université de Lorraine) as part of Séminaire de p hysique mathématique IPhT\n\nLecture held in Salle Claude Itzykson\, Bât . 774\, Orme des Merisiers.\n\nAbstract\nA meandric system of size n is a non-intersecting collection of closed loops in the plane crossing the real line in exactly 2n points (up to continuous deformation). In mathematical physics terms\, it can be seen as a loop model on a random lattice. Conne cted meandric systems are called meanders\, and their enumeration is a not orious hard problem in enumerative combinatorics. In this talk\, we discus s a different question\, raised independently by Goulden--Nica--Puder and Kargin: what is the number of connected components $cc(M_n)$ of a uniform random meandric system of size 2n? We prove that this number grows linear with n\, and concentrates around its mean value\, in the sense that $cc(M_ n)/n$ converges in probability to a constant. Our main tool is the definit ion of a notion of local convergence for meandric systems\, and the identi fication of the “quenched Benjamini--Schramm” limit of $M_n$. The latt er is the so-called infinite noodle\, a largely not understood percolation model recently introduced by Curien\, Kozma\, Sidoravicius and Tournier. \n\nOur main result has also a geometric interpretation\, regarding the Ha sse diagram $H_n$ of the non-crossing partition lattice $NC(n)$: informall y\, our result implies that\, in $H_n$\, almost all pairs of vertices are asymptotically at the same distance from each other. We use here a connect ion between $H_n$ and meandric systems discovered by Goulden\, Nica and Pu der. \n\nBased on joint work with Paul Thevenin (University of Vienna).\n LOCATION:https://researchseminars.org/talk/IPHT-PHM/21/ END:VEVENT END:VCALENDAR