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UID:www.tcs.tifr.res.in/event/991
DTSTAMP:20230914T125946Z
SUMMARY:How to tell a tale of two tails?
DESCRIPTION:Speaker: Parthanil Roy (Indian Statical Institute\nBangalore)\n
\nAbstract: \nAbstract: We study the extremes of branching random walks un
der the assumption that underlying Galton-Watson tree has infinite progeny
mean. It is assumed that the displacements are either regularly varying o
r have lighter tails. In the regularly varying case\, it is shown that the
point process sequence of normalized extremes converges to a Poisson rand
om measure. In the lighter-tailed case\, however\, the behaviour is much m
ore subtle\, and the scaling of the position of the rightmost particle in
the n-th generation depends on the family of stepsize distribution\, not j
ust its parameter(s). In all of these cases\, we discuss the convergence i
n probability of the scaled maxima sequence. Our results and methodology a
re applied to study the almost sure convergence in the context of cloud sp
eed for branching random walks with infinite progeny mean. The exact cloud
speed constants are calculated for regularly varying displacements and al
so for stepsize distributions having a nice exponential decay.\n\nThis tal
k is based on a joint work with Souvik Ray (Stanford University)\, Rajat S
ubhra Hazra (ISI Kolkata) and Philippe Soulier (Univ of Paris Nanterre). W
e will first review the literature (mainly\, the PhD thesis work of Ayan B
hattacharya) and then talk about the current work. Special care will be ta
ken so that a significant portion of the talk remains accessible to everyo
ne.\n
URL:https://www.tcs.tifr.res.in/web/events/991
DTSTART;TZID=Asia/Kolkata:20190909T160000
DTEND;TZID=Asia/Kolkata:20190909T170000
LOCATION:A-201 (STCS Seminar Room)
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