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
Mixing time for the Ising model : a uniform lower bound for all graphs
Consider Glauber dynamics for the Ising model on a graph of n vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least nlog n/f(Δ), where Δ is the maximum degree and f(Δ) = Θ(Δlog2Δ). Their result applies to more general spin systems, and in that generality, they showed that some dependence on Δ is necessary. In this paper, we focus on the ferromagnetic Ising model and prove that the mixing time of Glauber dynamics on any n-vertex graph is at least (1/4 + o(1))nlog n....
Modèles cinétiques à répartition discrète des vitesses et à invariance galiléenne
Non-local finite-size effects in the dimer model.
Numerical study of the 6-vertex model with domain wall boundary conditions
A Markov process converging to a random state of the 6-vertex model is constructed. It is used to show that a droplet of c-vertices is created in the antiferromagnetic phase and that the shape of this droplet has four cusps.
Odd cutsets and the hard-core model on
We consider the hard-core lattice gas model on and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds , the model exhibits multiple hard-core measures, thus improving the previous bound of given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...
On an invariance principle for phase separation lines
On disagreement percolation and maximality of the critical value for iid percolation.
On the approach to equilibrium for a polymer with adsorption and repulsion.
On the counting of fully packed loop configurations: some new conjectures.
On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
On the dimer problem and the Ising problem in finite 3-dimensional lattices.
On the doubly refined enumeration of alternating sign matrices and totally symmetric self-complementary plane partitions.
On the number of matchings in regular graphs.
One-dimensional random field Kac's model: weak large deviations principle.
One-dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.
Order parameters in -type spin quantum models with Gibbsian ground states.