Non domandarci la formula che mondi possa aprirti
Sì qualche storta sillaba e secca come un ramo
(E. Montale)
I am interested in the first place in the equilibrium statistical mechanics
of models with quenched randomness, in relaxation to equilibrium of Monte Carlo Markov Chains
and in stochastic evolution of discrete interfaces.
I am also interested in dimer models/random tilings of the plane
More specifically, themes on which I am presently working/have worked in the past are:
Localization-delocalization phenomena
for directed polymers in disordered media
- random (1+1)-dimensional copolymers at a selective interface
- pinning of directed polymers on a defect line
(e.g., pinning of (d+1)-dimensional polymers, (1+1)-dimensional interface
wetting problems, Poland-Scheraga model of DNA denaturation).
In particular: effect of disorder
on the localization transition (relevance/irrelevance of disorder)
- An only apparently unrelated question: exponential convergence rates for renewal sequences
Stochastic dynamics and relaxation to equilibrium
- Glauber dynamics of the Ising model at low temperature. More specifically: estimating the mixing time for the
dynamics with + boundary conditions.
- Stochastic dynamics of discrete interfaces/of random tilings/of dimer coverings.
Emergence of mean curvature evolution from microscopic models..
- Glauber dynamics of directed polymers and of (1+1)-dimensional and higher dimensional interfaces
(speed of convergence to equilibrium).
Spin glasses (mostly mean field)
- mean field models with infinite connectivity (Sherrington-Kirkpatrick model,
p-spin model)
- mean field models with finite connectivity, both on Poissonian (e.g.,
Viana-Bray model) and on non-Poissonian random graphs
- mean field spin glasses with additional short-range interactions ("Ising+Sherrington-Kirkpatrick" model)
- finite-dimensional spin glasses with long but finite interaction range (spin glass models
with Kac potentials)