BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sarah Penington (Univ. Bath\, U. K.) DTSTART:20211018T090000Z DTEND:20211018T110000Z DTSTAMP:20260421T173433Z UID:BPS/36 DESCRIPTION:Title: Gen ealogy of the N-particle branching random walk with polynomial tails\n by Sarah Penington (Univ. Bath\, U. K.) as part of Bangalore Probability S eminar\n\n\nAbstract\nThe N-particle branching random walk is a discrete t ime branching particle system with selection consisting of N particles loc ated on the real line. At every time step\, each particle is replaced by t wo offspring\, and each offspring particle makes a jump from its parent's location\, independently from the other jumps\, according to a given jump distribution. Then only the N rightmost particles survive\; the other part icles are removed from the system to keep the population size constant.\nI will discuss recent results and open conjectures about the long-term beha viour of this particle system when N\, the number of particles\, is large. In the case where the jump distribution has regularly varying tails\, bui lding on earlier work of J. Bérard and P. Maillard\, we prove that at a t ypical large time the genealogy of the population is given by a star-shape d coalescent\, and that almost the whole population is near the leftmost p article on the relevant space scale.\n\nBased on joint work with Matt Robe rts and Zsófia Talyigás.\n LOCATION:https://researchseminars.org/talk/BPS/36/ END:VEVENT END:VCALENDAR