We obtain product approximations to the law of particle systems with exclusion and Glauber dynamics in finite volume, by establishing a bound on the relative entropy between the law of the system and ...
The relative entropy method was developed by H.T. Yau in the 90’s to study the hydrodynamics of the Ginzburg-Landau model, and then adapted to several different dynamics. In this course (2 lectures,...
Nel seminario saranno presentati alcuni risultati riguardanti i sistemi interagenti ed in particolare il modello di Ising. I modelli interagenti saranno studiati sia dal punto di vista delle misure di...
We consider two interacting particle systems, Activated Random Walk and Oil and Water, which belong to the so-called class of Abelian networks. In these systems particles of two different types are pr...
The Miller-Abrahams random resistor network is used to study electron transport in amorphous solids. This resistor network is given by the complete random graph built on a marked homogeneous Poisson p...
In 2011, Benjamini, Kozma and Schapira introduced a “balanced excited random walk†in the 4-dimensional lattice. In 2016, a similar model was studied by Peres, Schapira and Sousi in the 3-dimensio...
Quantum analogs of classical random walks have been defined in quantum information theory as a useful concept to implement algorithms. Due to interference effects, statistical properties of quantum wa...
We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson clouds in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic f...
Homogenization of Hamilton-Jacobi equations with non-convex Hamiltonians in stationary ergodic random media is a largely open problem. In the last 5 years several classes of examples and counter-examp...
The measure theoretic generalization of oriented submanifolds of R^N of any dimension, are currents. One the most important theorem is the compactness criterium of Federer-Fleming. We try to prove and...
