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University of Cambridge > Talks.cam > Probability > Large deviations for the maximum of a branching random walk

## Large deviations for the maximum of a branching random walkAdd to your list(s) Download to your calendar using vCal - Nina Gantert (Technical University of Munich)
- Tuesday 12 March 2019, 14:00-15:00
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact Perla Sousi. We consider real-valued branching random walks and prove a large deviation result for the position of the rightmost particle. The position of the rightmost particle is the maximum of a collection of a random number of dependent random walks. We characterise the rate function as the solution of a variational problem. We consider the same random number of independent random walks, and show that the maximum of the branching random walk is dominated by the maximum of the independent random walks. For the maximum of independent random walks, we derive a large deviation principle as well. It turns out that the rate functions for upper large deviations coincide, but in general the rate functions for lower large deviations do not. As time permits, we also give some results about branching random walks in random environment. The talks is based on joint work with Thomas HÃ¶felsauer. This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
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