Pete Gábor (BME TTK Sztochasztika Tanszék):

       "Local time on the exceptional set of dynamical percolation,
        and the Incipient Infinite Cluster"
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In critical planar percolation, there are almost surely no infinite
clusters. However, if the configuration evolves according to a
continuous time Markov chain, there could be random exceptional
times when the origin is connected to infinity. A theorem of
Christophe Garban, Oded Schramm and myself from 2008 is
that such exceptional times do exist, and (for site percolation on the
triangular lattice) their Hausdorff dimension is 31/36.
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How does the cluster of the origin look like at exceptional times? In
joint work with Alan Hammond and Oded Schramm, we define a notion
of a typical exceptional time, and we show that, at such a time,
the law of the infinite cluster is Kesten's Incipient Infinite Cluster.
On the other hand, the cluster of the origin at the very first exceptional
time looks different.