Presented by:
Vincent Tassion
Date:
Monday 9th July 2018 - 14:35 to 15:20
Venue:
INI Seminar Room 1
Event:
Abstract:
We consider Boolean percolation in dimension d. Around
every point of a Poisson point process of intensity lambda, draw a ball of
random radius, independently for different points. We investigate the
connection probabilities in the subcritical regime and use the randomized
algorithm method to prove that the phase transition in lambda is sharp.
Interestingly, for this process, sharpness of the phase transition does not
imply exponential decay of connection probabilities in the subcritical regime,
and its meaning depends on the law of
the radii. In this talk, we will focus on this specific feature of Boolean
percolation.
This talk is based on a joint work with H. Duminil-Copin
and A. Raoufi.
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