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SUMMARY:Large deviations for the maximum of a branching random walk - Nina
  Gantert (Technical University of Munich)
DTSTART:20190312T140000Z
DTEND:20190312T150000Z
UID:TALK119038@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We consider real-valued branching random walks and prove a lar
 ge\ndeviation result for the position of the rightmost particle. The\nposi
 tion of the rightmost particle is the maximum of a collection of a\nrandom
  number of dependent random walks. We characterise the rate\nfunction as t
 he solution of a variational problem.\nWe consider the same random number 
 of independent random walks\, and show\nthat the maximum of the branching 
 random walk is dominated by the\nmaximum of the independent random walks.\
 nFor the maximum of independent random walks\, we derive a large deviation
 \nprinciple as well.\nIt turns out that the rate functions for upper large
  deviations\ncoincide\, but in general the rate functions for lower large 
 deviations\ndo not.\nAs time permits\, we also give some results about bra
 nching random walks\nin random environment.\n\nThe talks is based on joint
  work with Thomas Höfelsauer.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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