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UID:8598@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250304T143000
DTEND;TZID=Europe/Paris:20250304T153000
DTSTAMP:20250228T163054Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-211/
SUMMARY:Yoan TARDY (École polytechnique): Collisions of the supercritical 
 Keller-Segel particle system
DESCRIPTION:Yoan TARDY: We study a particle system naturally associated to 
 the 2-dimensional Keller-Segel equation.\nIt consists of N Brownian partic
 les in the plane\,\ninteracting through a binary attraction in θ/(Nr)\,\n
 where r stands for the distance between two particles.\nWhen the intensity
  θ of this attraction is greater than 2\,\nthis particle system explodes 
 in finite time.\nWe assume that N>3θ and study in details what happens ne
 ar explosion.\nThere are two slightly different scenarios\,\ndepending on 
 the values of N and θ\, here is one:\nat explosion\, a cluster consisting
  of precisely k0 particles emerges\,\nfor some deterministic k0≥7 depend
 ing on N and θ.\nJust before explosion\, there are infinitely many (k0−
 1)-ary collisions.\nThere are also infinitely many (k0−2)-ary collisions
  before each (k0−1)-ary collision.\nAnd there are infinitely many binary
  collisions before each (k0−2)-ary collision.\nFinally\, collisions of s
 ubsets of 3\,…\,k0−3 particles never occur.\nThe other scenario is sim
 ilar except that there are no (k0−2)-ary collisions.
CATEGORIES:Séminaire,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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