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BEGIN:VEVENT
DTSTAMP:20191002T121344Z
DTSTART:20191023T130000Z
DTEND:20191023T140000Z
SUMMARY:Marton Balazs (Bristol) - Nonexistence of bi-infinite geodesics i
n exponential last passage percolation - a probabilistic way
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}zq7-k198c56
o-6tw6j1
DESCRIPTION:Marton Balazs(Bristol) will give a talk at Probability semi
nar. \n\nAbstract:\nTake a point on the 2-dimensional integer lattice an
d another one North-East from the first. Place i.i.d. Exponential weight
s on the vertices of the lattice\; the point-to-point geodesic between t
he two points is the a.s. unique path of North and East steps that colle
cts the maximal sum of these weights.\n\nA bi-infinite geodesic is a dou
bly infinite North-East path such that any segment between two of its po
ints is a point-to-point geodesic. We show that this thing a.s. does not
exist (except for the trivial case of the coordinate axes). The intuiti
on is roughly this: transversal fluctuations of a point-to-point geodesi
c are in the order of the 2/3rd power of its length\, which becomes infi
nite for a bi-infinite geodesic. This and coalescence of geodesics resul
t in not seeing this path anywhere near the origin which\, combined with
translation invariance\, a.s. excludes its existence.\n\nOne needs to m
ake this more quantitative to prove that even after taking the union for
all possible directions we cannot see a bi-infinite geodesic\, a progra
m sketched by Newman. This has recently been completed rigorously by Bas
u\, Hoffman and Sly with inputs from integrable probability. In this wor
k we instead build on purely probabilistic arguments\, such as couplings
and maxima of drifted random walks\, to arrive to this result.\n\nThis
is a joint work in progress with Ofer Busani and Timo Seppäläinen
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:G108\, Alan Turing Building\, Manchester
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