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SUMMARY:Limit of the Right-Most Position of a Modified Branching Random Wa
lk
DTSTART;VALUE=DATE-TIME:20191022T103000Z
DTEND;VALUE=DATE-TIME:20191022T113000Z
DTSTAMP;VALUE=DATE-TIME:20200928T002537Z
UID:indico-event-7408@cern.ch
DESCRIPTION:Abstract: In this talk\, we consider a modification of the usu
al Branching Random Walk (BRW)\, where at the last step we give certain di
splacements which may be different from the increments. Under very minimal
assumption on the underlying point process we show that the maximum displ
acement converges to a limit after only an appropriate centering. We furth
er show that the centering term is $c_1 n + c_2 \\log n$ and give explicit
formula for the constants $c_1$ and $c_2$. If the underlying point proces
s is i.i.d. displacements then we show that $c_1$ is exactly same and $c_2
$ is $1/3$-of the corresponding constants of the usual BRW. Our proofs are
based on a novel method of coupling with a more well studied process know
n as the smoothing transformation.\n\n[This is a joint work with Partha Pr
atim Ghosh]\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?conf
Id=7408
LOCATION: A-201 (STCS Seminar Room)
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7408
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