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CATEGORIES:Probability
SUMMARY:The criticality of a randomly-driven front - Amir
Dembo (Stanford)
DTSTART;TZID=Europe/London:20180515T140000
DTEND;TZID=Europe/London:20180515T150000
UID:TALK97882AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/97882
DESCRIPTION:Consider independent continuous-time random walks
on the integers to the right of a front R(t). Star
ting at R(0)=0\, whenever a particle attempts to j
ump into the front\, the latter instantaneously ad
vances k steps to the right\, absorbing all partic
les along its path. Sly (2016) resolves the questi
on 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 kn
own about the large t asymptotic of R(t) at critic
al density 1. In a joint work with L-C Tsai\, for
the variant model with k taken as the minimal rand
om integer such that exactly k particles are absor
bed by the move of R(t)\, we obtain both scaling e
xponent and the random scaling limit for the front
at the critical density 1. Our result unveils a r
arely seen phenomenon where the macroscopic scalin
g exponent is sensitive to the initial local fluct
uations (with the scaling limit oscillating betwee
n instantaneous super and sub-critical phases).\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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