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Thursday, 23.01.2020 | 14.00 - 16.00 Uhr | A3.339

Oberseminar Stochastik: Prof. Dr. Matthias Birkner, Mainz - Low-dimensional lonely branching random walks die out


We consider an interacting particle system where each particle moves
as an independent random walk and undergoes critical binary branching
when it is alone. We prove clustering, i.e. local extinction combined
with increasingly rare regions of diverging density, whenever the
symmetrized walk is recurrent. Furthermore, the same result holds if
additional branching is allowed when the walk is not alone. This can
be viewed as a 'microscopic' complement of analogous results by Cox,
Fleischmann and Greven (1996) for a class of continuous-mass models.

Joint work with Rongfeng Sun (NUS, Singapore)

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