BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Guilherme Silva (Universidade de São Paulo) DTSTART:20200903T140000Z DTEND:20200903T150000Z DTSTAMP:20260423T021245Z UID:JIPS/5 DESCRIPTION:Title: Per iodic TASEP: when integrable systems meet integrable probability (once aga in)\nby Guilherme Silva (Universidade de São Paulo) as part of Junior Integrable Probability Seminar\n\n\nAbstract\nIt is well-known that the T racy-Widom distributions admit representations involving solutions to part icular integrable systems. Other marginals of the KPZ fixed point\, such a s the Airy2 process\, also admit similar representations. And very recentl y\, first by Quastel and Remenik and shortly afterwards by Le Doussal\, st atistics of the KPZ fixed point were found to be connected to the KP equat ion.\n\nIn this talk\, we plan to overview some analogue connections\, but now for distributions of the periodic TASEP (pTASEP)\, which are believed to be the universal analogue of the KPZ universality class for periodic s etup. For the step periodic initial condition\, we compare the limiting on e-point distribution of the pTASEP with the GUE Tracy-Widom distribution\, highlighting the key features that allow to connect both of them to coupl ed systems of mKdV and heat equations. We also discuss some asymptotic pro perties of this limiting distribution\, showing that it interpolates betwe en the GUE Tracy-Widom and a Gaussian. For pTASEP with general initial con dition\, we also explain how very few analytic aspects of its limiting one -point distribution give a connection with the KP equation\, in analogous way to Quastel-Remenik’s mentioned result. This talk is based on joint w ork with Jinho Baik (University of Michigan) and Zhipeng Liu (University o f Kansas). Time permitting\, we also briefly discuss a work in progress wi th Jinho Baik and Andrei Prokhorov (University of Michigan)\, greatly exte nding the mentioned results to multipoint distributions.\n LOCATION:https://researchseminars.org/talk/JIPS/5/ END:VEVENT END:VCALENDAR