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UID:9331@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20261215T143000
DTEND;TZID=Europe/Paris:20261215T153000
DTSTAMP:20261103T163509Z
URL:https://www.i2m.univ-amu.fr/evenements/cutoff-phenomenon-for-the-decou
 pling-random-walks-on-the-complete-graph/
SUMMARY:Ons RAMEH (Sorbonne Université): Cutoff Phenomenon for the Decoupl
 ing Random Walks on the Complete Graph
DESCRIPTION:Ons RAMEH: In this talk\, we introduce a new model called “de
 coupling random walks” (DRW)\, as an auxiliary model \nto the Binomial S
 plitting process. It consists of a system of k = N^a continuous-time rando
 m walks \non the complete graph with N vertices. Particles starting from d
 istinct vertices evolve independently\, \nwhereas particles starting from 
 the same vertex do not: they share the same clock and the same chosen neig
 hbour\, \nand the decisions of whether to jump are sampled jointly. These 
 dependencies progressively disappear \nas particles separate\, and eventua
 lly\, all particles evolve independently. \n\nAlthough DRW differs from in
 dependent random walks only by this temporary dependence\, its mixing beha
 vior \nturns out to be significantly more complex. Indeed\, we show that D
 RW exhibits a cutoff phenomenon at time \nC(a) log(N)\, where the mapping 
 a ↦ C(a) is non-differentiable at four transition points\, leading to fi
 ve \ndistinct regimes. \n\nThis is a joint work with P. Caputo\, M. Quattr
 opani\, and F. Sau. \n
CATEGORIES:Séminaire,ALEA,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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DTSTART:20261025T020000
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