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CATEGORIES:Probability
SUMMARY:Large deviations for the maximum of a branching ra
ndom walk - Nina Gantert (Technical University of
Munich)
DTSTART;TZID=Europe/London:20190312T140000
DTEND;TZID=Europe/London:20190312T150000
UID:TALK119038AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/119038
DESCRIPTION:We consider real-valued branching random walks and
prove a large\ndeviation result for the position
of the rightmost particle. The\nposition of the ri
ghtmost particle is the maximum of a collection of
a\nrandom number of dependent random walks. We ch
aracterise the rate\nfunction as the solution of a
variational problem.\nWe consider the same random
number of independent random walks\, and show\nth
at the maximum of the branching random walk is dom
inated by the\nmaximum of the independent random w
alks.\nFor the maximum of independent random walks
\, we derive a large deviation\nprinciple as well.
\nIt turns out that the rate functions for upper l
arge deviations\ncoincide\, but in general the rat
e functions for lower large deviations\ndo not.\nA
s time permits\, we also give some results about b
ranching random walks\nin random environment.\n\nT
he talks is based on joint work with Thomas HÃ¶fels
auer.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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