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DTSTAMP:20260424T140906Z
UID:1702915200@ist.ac.at
DTSTART:20231218T170000
DTEND:20231218T180000
DESCRIPTION:Speaker: Zsofia Talyigas\nhosted by M. Beiglböck\, N. Berestyc
 ki\, L. Erdös\, J. Maas\, F. Toninelli\, E. Schertzer\nAbstract: The N-pa
 rticle branching random walk is a discrete time branching particle system 
 with selection. We have N particles located on the real line at all times.
  At every time step each particle is replaced by two offspring\, and each 
 offspring particle makes a jump of non-negative size from its parent's loc
 ation\, independently from the other jumps\, according to a given jump dis
 tribution. Then only the N rightmost particles survive\; the other particl
 es are removed from the system to keep the population size constant. This 
 process shows very different behaviours with different jump distributions 
 in terms of speed and genealogy. The speed in the ‘light-tailed’ case 
 (when the jump distribution has some exponential moments) was studied by B
 érard and Gouéré\, and the polynomial-tailed case was investigated in t
 he work of Bérard and Maillard. As these two cases are significantly diff
 erent from each other\, we aimed to fill the gap with our result on the in
 termediate stretched exponential case. We describe the first order and giv
 e lower and upper bounds on the second order of the asymptotic speed as th
 e number of particles N goes to infinity. If time allows I will also discu
 ss our genealogy result in the polynomial case\, which says that at a typi
 cal large time the genealogy of the population is given by a star-shaped c
 oalescent. The talk is based on joint work with Sarah Penington and Matthe
 w Roberts. 
LOCATION:Mondi 2 (I01.01.008)\, Central Building\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at 
SUMMARY:Zsofia Talyigas: Different behaviours of the N-particle branching r
 andom walk
URL:https://talks-calendar.ista.ac.at/events/4647
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