| 概要 | The cover time is a fundamental parameter of a finite graph and
has been extensively studied. It is defined as the first time random
walk on a graph has visited every vertex. The first order asymptotics of
the cover time is known for many families of graphs. Much less is known
about the fluctuations. In this talk I will present some recent results
on fluctuations, including the resolution of a conjecture stating that
the fluctuations in the discrete torus of dimension at least 3 (an
important example) are governed by the Gumbel extreme value distribution. |