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We consider diffusion of independent molecules in an insulated Euclidean domain with unknown diffusivity parameter. At a random time and position, the molecules may bind and stop diffusing in dependence of a given `binding potential'. The…
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
A new technique for proving uniqueness of martingale problems is introduced. The method is illustrated in the context of elliptic diffusions in $R^d$.
An analysis of the random lattice gas in the annealed limit is presented. The statistical mechanics of disordered lattice systems is briefly reviewed. For the case of the lattice gas with an arbitrary uniform interaction potential and…
We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
A common wisdom posits that transports of conserved quantities across clean nonintegrable quantum systems at high temperatures are diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter…
We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining hypocoercivity method in [37] and relative entropy method in [25], we are able to overcome the degeneracy of diffusion…
We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in…
Quantum lattice systems are rigorously studied at low temperatures. When the Hamiltonian of the system consists of a potential (diagonal) term and a - small - off-diagonal matrix containing typically quantum effects, such as a hopping…
A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of…
The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the…
Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a L\'evy process, and the interaction between particles is determined by the…
We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation…
We study a class of Lindblad equation on finite-dimensional fermionic systems. The model is obtained as the continuous-time limit of a repeated interaction process between fermionic systems with quadratic Hamiltonians, a setup already used…
Determining the dynamics of interacting integrable many-particle quantum systems at finite times after homogeneous quantum quenches is a long-standing challenge. We present a Monte Carlo sampling scheme that numerically evaluates the…
Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has…
In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model I begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in…
We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…
We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of…