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CATEGORIES:Probability
SUMMARY:Empirical measures\, geodesic lengths\, and a vari
ational formula in first-passage percolation - Eri
k Bates\, University of Wisconsin-Madison
DTSTART;TZID=Europe/London:20211102T140000
DTEND;TZID=Europe/London:20211102T150000
UID:TALK164056AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/164056
DESCRIPTION:We consider the standard first-passage percolation
model on Z^d\, in which each edge is assigned an
i.i.d. nonnegative weight\, and the passage time b
etween any two points is the smallest total weight
of a nearest-neighbor path between them. This in
duces a random ``disorderedâ€ť geometry on the latti
ce. Our primary interest is in the empirical meas
ures of edge-weights observed along geodesics in t
his geometry\, say from 0 to [n\\xi]\, where \\xi
is a fixed unit vector. For various dense families
of edge-weight distributions\, we prove that thes
e measures converge weakly to a deterministic limi
t as n tends to infinity. The key tool is a new va
riational formula for the time constant. In this t
alk\, I will derive this formula and discuss its i
mplications for the convergence of both empirical
measures and lengths of geodesics.
LOCATION:MR12 Centre for Mathematical Sciences
CONTACT:Sourav Sarkar
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