BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Josué Corujo (Université Paris Dauphine (CEREMADE)) DTSTART:20210608T130000Z DTEND:20210608T140000Z DTSTAMP:20260423T021302Z UID:POSemP/7 DESCRIPTION:Title: S pectrum and ergodicity of a neutral multi-allelic Moran model\nby Josu é Corujo (Université Paris Dauphine (CEREMADE)) as part of Pisa Online S eminar in Probability\n\n\nAbstract\nWe will present some recent results o n the study of a neutral\nmulti-allelic Moran model\, which is a finite co ntinuous-time Markov\nprocess. For this process\, it is assumed that the i ndividuals interact\naccording to two processes: a mutation process where they mutate\nindependently of each other according to an irreducible rate matrix\, and\na Moran type reproduction process\, where two individuals ar e uniformly\nchosen\, one dies and the other is duplicated. During this ta lk we will\ndiscuss some recent results for the spectrum of the generator of the\nneutral multi-allelic Moran process\, providing explicit expressio ns for\nits eigenvalues in terms of the eigenvalues of the rate matrix tha t\ndrives the mutation process. Our approach does not require that the\nmu tation process be reversible\, or even diagonalizable. Additionally\, we\n will discuss some applications of these results to the study of the\nspeed of convergence to stationarity of the Moran process for a process\nwith g eneral mutation scheme. We specially focus on the case where the\nmutation scheme satisfies the so called "parent independent" condition\,\nwhere (a nd only where) the neutral Moran model becomes reversible. In\nthis later case we can go further and prove the existence of a cutoff\nphenomenon for the convergence to stationarity.\n\nThis presentation is based on a recen tly submitted work\, for which a\npreprint is available at https://arxiv.o rg/abs/2010.08809.\n LOCATION:https://researchseminars.org/talk/POSemP/7/ END:VEVENT END:VCALENDAR