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CATEGORIES:Probability
SUMMARY:The Slow Bond Problem - Sourav Sarkar (Cambridge)
DTSTART;TZID=Europe/London:20211012T140000
DTEND;TZID=Europe/London:20211012T150000
UID:TALK163708AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/163708
DESCRIPTION:Whether a localized microscopic defect will affect
the macroscopic behaviour of a system is a fundam
ental question in statistical mechanics. For the T
otally Asymmetric Simple Exclusion Process (TASEP)
on $\\mathbb{Z}$\, this problem was originally po
sed by Janowsky and Lebowitz and became famous as
the ``slow-bondâ€ť 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 macros
copic current? Different groups of physicists\, us
ing a range of heuristics and numerical simulation
s\, reached opposing conclusions on whether the cr
itical value of $\\epsilon$ is $0$. This was ultim
ately 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 wh
y it was so challenging to predict on the basis of
numerical simulations. In particular\, we show th
at with the effect of the perturbation tends to 0
faster than any polynomial. Our proof focuses on t
he Last Passage Percolation formulation of TASEP.
The talk is based on joint works with Allan Sly an
d Lingfu Zhang.
LOCATION:MR12 Centre for Mathematical Sciences
CONTACT:Jason Miller
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