Lattice field theory with the sign problem and the maximum entropy method.
Limit theorems for the painting of graphs by clusters
We consider a generalization of the so-called divide and color model recently introduced by Häggström. We investigate the behavior of the magnetization in large boxes of the lattice and its fluctuations. Thus, Laws of Large Numbers and Central Limit Theorems are proved, both quenched and annealed. We show that the properties of the underlying percolation process deeply influence the behavior of the coloring model. In the subcritical case, the limit magnetization is deterministic and the Central...
Limit Theorems for the painting of graphs by clusters
We consider a generalization of the so-called divide and color model recently introduced by Häggström. We investigate the behavior of the magnetization in large boxes of the lattice and its fluctuations. Thus, Laws of Large Numbers and Central Limit Theorems are proved, both quenched and annealed. We show that the properties of the underlying percolation process deeply influence the behavior of the coloring model. In the subcritical case, the limit magnetization is deterministic and the Central Limit...
Lipschitz percolation.
Local statistics of lattice dimers
Localisation for non-monotone Schrödinger operators
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schrödinger operators with non-monotone random potentials, on the -dimensional lattice. Our results include dynamical localisation, i.e. exponentially decaying bounds on the transition amplitude in the mean. They are derived through the study of fractional moments of the resolvent, which are finite due to resonance-diffusing effects of the disorder. One of the byproducts of the analysis...
Logarithmic Sobolev inequalities for unbounded spin systems revisited