BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alan Hammond (UC Berkeley) DTSTART:20210312T173000Z DTEND:20210312T183000Z DTSTAMP:20260423T005718Z UID:PatC/29 DESCRIPTION:Title: St ability and chaos in dynamical last passage percolation\nby Alan Hammo nd (UC Berkeley) as part of Probability and the City Seminar\n\n\nAbstract \nMany complex statistical mechanical models have intricate energy landsca pes. The ground state\, or lowest energy state\, lies at the base of the d eepest valley. In examples such as spin glasses and Gaussian polymers\, th ere are many valleys\; the abundance of near-ground states (at the base of valleys) indicates the phenomenon of chaos\, under which the ground state alters profoundly when the model's disorder is slightly perturbed. Indeed \, a monograph of Sourav Chatterjee from 2014 establishes that\, for a cla ss of models of Gaussian disorder\, this abundance of competing minimizers is accompanied both by a rapid outset of chaos under perturbation of the system by noise\, and by the effect of super-concentration\, in which mod el statistics have lower variance than in classical scenarios\, for which a central limit theorem may apply.\n\nIn this talk\, a recent investigatio n\, jointly undertaken with Shirshendu Ganguly\, of a natural dynamics for a model of planar last passage percolation will be discussed. Robust prob abilistic and geometric technique permits a very quantified analysis of th e presence of close rivals in energy to the ground state for the static ve rsion of the model\; consequently\, the order of the scale that heralds th e transition from stability to chaos for the dynamical model is identified . The tools that drive the investigation include harmonic analytic techniq ue present in Chatterjee's work\, and the use of Brownian Gibbs resampling analysis for random ensembles of curves naturally associated to last pass age percolation via the Robinson-Schensted-Knuth correspondence.\n LOCATION:https://researchseminars.org/talk/PatC/29/ END:VEVENT END:VCALENDAR