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DTSTAMP:20260408T225103Z
UID:1621351800@ist.ac.at
DTSTART:20210518T173000
DTEND:20210518T181500
DESCRIPTION:Speaker: Nicolas Curien\nhosted by M. Beiglböck\, N. Berestyck
 i\, L. Erdös\, J. Maas\, F. Toninelli\nAbstract: Consider a uniform Cayle
 y tree Tn with n vertices and let m cars arrive sequentially\, independent
 ly\, and uniformly on its vertices. Each car tries to park on its arrival 
 node\, and if the spot is already occupied\, it drives towards the root o
 f the tree and park as soon as possible. Using combinatorial enumeration\
 , Lackner & Panholzer established a phase transition for this process wh
 en m is approximately n/2 . We couple this model with a variation of the 
 classical Erdös–Rényi random graph process. This enables us to complet
 ely describe the phase transition for the size of the components of parked
  cars using a modification of the standard multiplicative coalescent which
  we named the frozen multiplicative coalescent. The geometry of critical p
 arked clusters in the parking process is also studied. Those trees are ver
 y different from usual random trees and should converge towards the growth
 -fragmentation trees canonically associated to 3/2-stable process that alr
 eady appeared in the study of random planar maps. The talk is based on jo
 int work with Alice Contat.
LOCATION:Online via Zoom\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Nicolas Curien: Parking on Cayley trees & Frozen Erdös-Rényi
URL:https://talks-calendar.ista.ac.at/events/3124
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