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SUMMARY:The Slow Bond Problem - Sourav Sarkar (Cambridge)
DTSTART:20211012T130000Z
DTEND:20211012T140000Z
UID:TALK163708@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:Whether a localized microscopic defect will affect the macrosc
 opic behaviour of a system is a fundamental question in statistical mechan
 ics. For the Totally Asymmetric Simple Exclusion Process (TASEP) on $\\mat
 hbb{Z}$\, this problem was originally posed by Janowsky and Lebowitz and b
 ecame famous as the ``slow-bond” problem. If the wait time of jump for a
  particle at the origin is increased from an exponential with rate $1$ to 
 that with rate $1-\\epsilon$\, is this effect detectable in the macroscopi
 c current? Different groups of physicists\, using a range of heuristics an
 d numerical simulations\, reached opposing conclusions on whether the crit
 ical value of $\\epsilon$ is $0$. This was ultimately resolved rigorously 
 in Basu-Sidoravicius-Sly which established that $\\epsilon_c=0$. In this t
 alk\, we will study the effect of the current as $\\epsilon$ tends to $0$ 
 and in doing so explain why it was so challenging to predict on the basis 
 of numerical simulations. In particular\, we show that with the effect of 
 the perturbation tends to 0 faster than any polynomial. Our proof focuses 
 on the Last Passage Percolation formulation of TASEP. The talk is based on
  joint works with Allan Sly and Lingfu Zhang.
LOCATION:MR12  Centre for Mathematical Sciences
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