On the
Potential-theoretic
Approach to
Metastability
This talk is a
supplement to the
mini-course by E.
Scoppola and A.
Gaudilliere. I
describe recent
joint work with A.
Bovier and C.
Spitoni that adopts
a
potential-theoretic
perspective to
compute metastable
transition times for
Ising spins subject
to Glauber spin-fip
dynamics (a dynamic
model for
magnetisation) and
for lattice
particles subject to
Kawasaki hopping
dynamics (a dynamic
model for
condensation).
I will focus on
systems at low
temperature in the
metastable phase,
i.e., when all
droplets (= clusters
of plus-spins or
clusters of
particles) are small.
Both small systems
and large systems
are of interest. I
will show that sharp
upper and lower
bounds can be
obtained for the
average nucleation
time, i.e., the
first time a
critical droplet
appears somewhere in
the system, via a
calculation of
associated
capacities between
metastable sets of
configurations. This
leads into
interesting
variational
computations,
exploiting geometric
aspects of droplets
as well.