Presented by:
Mircea Petrache
Date:
Monday 26th November 2018 - 11:00 to 12:30
Venue:
INI Seminar Room 2
Abstract:
If N points interact by Coulomb 2-point repulsion and under
a "confining" potential V(x)=|x|^2, as N goes to infinity they spread
uniformly in a ball. This is a typical problem about "energy-minimizing
configurations".
What is the simplest problem that we get if we move
from variational problems on N-point configurations, to variational problems on
measures on N-point configurations? In that case there is a more natural
replacement of the "confinement", previously played by V(x): it is to
just "fix the 1-point marginal" of our measure on configurations. We
obtain a generalization of optimal transport, for N-marginals instead of the
usual 2-marginals case.
In my talk I'll describe the above two types of
large-N asymptotics problems in more detail, I'll overview the techniques that
we know, and I'll mention some parts of this subject that we currently don't
understand.