Date/heure
22 novembre 2018
10:45 - 11:45
Oratrice ou orateur
Siamak Taati
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
In a quasicrystal, the arrangement of the atoms is highly ordered (as
in an ordinary crystal) but non-periodic (unlike in a crystal). There
are various mathematical challenges in connection with quasicrystals.
From the point of view of statistical mechanics, the major open
problem is to provide a mathematical explanation of the formation and
stability of quasicrystals in presence of thermal fluctuations. In
this talk, I will present a (toy) lattice gas model with finite-range
interactions that has stable quasicrystal phases at positive
temperature (i.e., Gibbs measures supported at perturbations of
non-periodic tilings). The construction is based on old results on
cellular automata and tilings, in particular, a method of simulating
one cellular automaton with another that is resilient against noise,
and the existence of aperiodic sets of Wang tiles that are
deterministic in one direction.