BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Romain Panis (Institut Camille Jordan) DTSTART:20261006T140000Z DTEND:20261006T150000Z DTSTAMP:20260624T232937Z UID:IAMP_seminars/199 DESCRIPTION:Title: A random walk approach to high-dimensional critical phenomena\ nby Romain Panis (Institut Camille Jordan) as part of One world IAMP mathe matical physics seminar\n\n\nAbstract\nOne of the main goals of statistica l mechanics is to understand critical phenomena of lattice models. This ca n be achieved by computing critical exponents\, which govern the universal behaviour of the model at and near its critical point. This task is gener ally difficult due to the intricate interplay between model-specific featu res and the underlying graph geometry.\n\nA striking observation was made in the 20th century: above the upper critical dimension d_c\, the geometry becomes irrelevant and critical exponents adopt their mean-field values ( as on Cayley trees or complete graphs). Classical approaches—renormaliza tion group\, differential inequalities\, and the lace expansion—are powe rful but model-specific and technically demanding. We present a new\, unif ied\, probabilistic\, and relatively simple proof of mean-field critical b ehaviour for high-dimensional models containing a small parameter. Applica tions include spin systems and self-avoiding walks in dimensions d>4\, per colation in dimensions d>6\, and lattice trees in dimensions d>8. \n\nJoin t work with Hugo Duminil-Copin\, Aman Markar\, and Gordon Slade.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/199/ END:VEVENT END:VCALENDAR