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PRODID:-//Ashoka University - ECPv6.18.2//NONSGML v1.0//EN
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X-WR-CALNAME:Ashoka University
X-ORIGINAL-URL:https://www.ashoka.edu.in
X-WR-CALDESC:Events for Ashoka University
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DTSTART:20180101T000000
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BEGIN:VEVENT
DTSTART;TZID=UTC:20191112T163000
DTEND;TZID=UTC:20191112T173000
DTSTAMP:20211006T195417Z
CREATED:20211006T195417Z
LAST-MODIFIED:20211006T195417Z
UID:20119-1573576200-1573579800@www.ashoka.edu.in
SUMMARY:Percolation on Hyperbolic Groups
DESCRIPTION:Abstract: We study first passage percolation (FPP) in a Gromov-hyperbolic group G with boundary equipped with the Patterson-Sullivan measure. We associate an .i.d. collection of random passage times to each edge of a  Cayley graph of G\, and investigate classical questions about the asymptotics of first passage time as well as the geometry of geodesics in the FPP metric. Under suitable conditions on the passage time distribution\, we show that the ‘velocity’ exists in almost every direction\, and is almost surely constant by ergodicity of the G-action on the boundary. For every point on the boundary\, we also show almost sure coalescence of any two geodesic rays directed towards the point. Finally\, we show that the variance of the first passage time grows linearly with word distance along with word geodesic rays in every fixed boundary direction.
URL:https://www.ashoka.edu.in/event/percolation-on-hyperbolic-groups/
CATEGORIES:Online Event
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