Schramm-Loewner Evolution (SLE) is the solution of the
classical Loewner equation in complex analysis with a stochastic driving
function defined in terms of a one-dimensional Brownian motion. Since it
was introduced for the first time by Odded Schramm in 1999, SLE has been
intensively studied by mathematicians and physicists. It has been proved
or conjectured to be the scaling limits of various lattice models in
statistical physics. In this talk, we will discuss the average
generalized integral means spectrum of the whole-plane variant of SLE.
This generalized spectrum has been introduced to give a unified
framework to study the (expected) standard integral means spectrum of
various functions in the SLE context. We will introduce the definition
of the average generalized integral means spectrum of whole-plan SLE and
a conjecture about the values of this spectrum. We then talk about the
results so far obtained that confirm this conjecture and the Maximum
principle method that were used to derive these results. This talk is
based on joint works with Bertrand Duplantier, Thanh Binh Le and Michel
Zinsmeister.
Meeting ID: 852 4277 3200
Passcode: 103121