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UID:www.tcs.tifr.res.in/event/737
DTSTAMP:20230914T125936Z
SUMMARY:Coarse Geometry of Random Metric Subspaces of Euclidean Spaces and
Connections to Dependent Percolation
DESCRIPTION:Speaker: Riddhipratim Basu (Stanford University\nDepartment of
Mathematics\nBuilding 380\, 450 Serra Mall\nStanford\, CA 94305\nUnited St
ates of America)\n\nAbstract: \nTwo metric spaces are said to be quasi iso
metric if their metrics are equivalent up to multiplicative and additive c
onstants. This notion\, introduced by Gromov (1981) for\ngroups and more g
enerally by Kanai (1985) has proved to be important in coarse geometry. Th
ere has been recent interest in understanding the coarse geometry of rando
m subgraphs of Cayley graphs and in particular whether or not two independ
ent copies of random metric spaces with identical distribution are quasi i
sometric. I shall describe a sequence of works (joint with Allan Sly and V
ladas Sidoravicius) that address questions of this flavour for random subs
ets of Euclidean Spaces. In particular we show that two copies of Bernoull
i percolation on $\\mathbb{Z}$\; i.e.\, when each element of $\\mathbb{Z}$
is included in the random subset independently and with equal probability
\, are almost surely quasi isometric. We develop a multi-scale framework f
lexible enough to tackle a number of such embedding questions including so
me closely related natural questions in dependent percolation. I shall als
o discuss an approach to higher dimensional extensions and a number of int
eresting open questions.\n \n
URL:https://www.tcs.tifr.res.in/web/events/737
DTSTART;TZID=Asia/Kolkata:20161228T160000
DTEND;TZID=Asia/Kolkata:20161228T170000
LOCATION:AG-69
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