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SUMMARY:Phase transition for the late points of random walk - Perla Sousi
(University of Cambridge)
DTSTART;VALUE=DATE-TIME:20240115T140000Z
DTEND;VALUE=DATE-TIME:20240115T150000Z
UID:https://talks.ox.ac.uk/talks/id/056f62ce-4ef0-4571-8511-b157d3ea8c6f/
DESCRIPTION:Let X be a simple random walk in \\mathbb{Z}_n^d with d\\geq 3
and let t_{\\rm{cov}} be the expected time it takes for X to visit all ve
rtices of the torus. In joint work with PrÃ©vost and Rodriguez we study th
e set \\mathcal{L}_\\alpha of points that have not been visited by time \\
alpha t_{\\rm{cov}} and prove that it exhibits a phase transition: there e
xists \\alpha_* so that for all \\alpha>\\alpha_* and all \\epsilon>0 ther
e exists a coupling between \\mathcal{L}_\\alpha and two i.i.d. Bernoulli
sets \\mathcal{B}^{\\pm} on the torus with parameters n^{-(a\\pm\\epsilon)
d}with the property that \\mathcal{B}^-\\subseteq \\mathcal{L}_\\alpha\\su
bseteq \\mathcal{B}^+ with probability tending to 1 as n\\to\\infty. When
\\alpha\\leq \\alpha_*\, we prove that there is no such coupling. \nSpeake
rs:\nPerla Sousi (University of Cambridge)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/056f62ce-4ef0-4571-8511-b157d3ea8c6f/
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DESCRIPTION:Talk:Phase transition for the late points of random walk - Pe
rla Sousi (University of Cambridge)
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