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SUMMARY:The criticality of a randomly-driven front - Amir Dembo (Stanford)
DTSTART:20180515T130000Z
DTEND:20180515T140000Z
UID:TALK97882@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Consider independent continuous-time random walks on the integ
 ers to the right of a front R(t). Starting at R(0)=0\, whenever a particle
  attempts to jump into the front\, the latter instantaneously advances k s
 teps to the right\, absorbing all particles along its path. Sly (2016) res
 olves the question of Kesten and Sidoravicius (2008)\, by showing that for
  k=1 the front R(t) advances linearly once the particle density exceeds 1\
 , but little is known about the large t asymptotic of R(t) at critical den
 sity 1. In a joint work with L-C Tsai\, for the variant model with k taken
  as the minimal random integer such that exactly k particles are absorbed 
 by the move of R(t)\, we obtain both scaling exponent and the random scali
 ng limit for the front at the critical density 1. Our result unveils a rar
 ely seen phenomenon where the macroscopic scaling exponent is sensitive to
  the initial local fluctuations (with the scaling limit oscillating betwee
 n instantaneous super and sub-critical phases).\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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