[Probability] Probability Forum

Zygouras, Nikolaos N.Zygouras at warwick.ac.uk
Tue May 11 01:07:16 BST 2010

  Dear All,

    in the probability forum, tomorrow, Wednesday noon at A1.01

   Augusto Teixeira (ETH):

   "Giant vacant component left by a random walk in a random d-regular graph"

Abstract: We will discuss the trajectory of a simple random walk on a
random d-regular graph of n vertices, with d > 2. More precisely, we
investigate percolative properties of the set of vertices not visited
by the walk until time un, where u > 0 is a fixed positive parameter.
We show that this so-called `vacant set' exhibits a phase transition
in u in the following sense: there exists an explicitly computable
threshold u^* \in (0,\infty) such that, if u < u^*, with high
probability as n grows, the largest component of the vacant set has a
volume of order n, and if u > u^*, then it has a volume of order log
n. The critical value u^* coincides with the critical intensity of a
random interlacement process on an infinite d-regular tree.

   The following two wednedays there will be no probability forum due to the
 Midlands Probability Seminars.

   Best, NIkos.
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