Gioia Carinci

Duality for stochastic models of transport

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particle densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites.The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Long-range correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.

Super-hydrodynamic limit in interacting particle systems

This paper is a follow-up of the work initiated in (Arab J Math, 2014), where we investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two further results: first we characterize the stationary states on the hydrodynamic time scale as a family of linear macroscopic profiles parameterized by their mass. Then we prove that beyond hydrodynamics there exists a longer time scale where the evolution becomes random. On such a super-hydrodynamic scale the particle system is at each time close to the stationary state with same mass and the mass fluctuates performing a Brownian motion reflected at the origin.

Asymmetric Stochastic Transport Models with \({\mathscr {U}}_q(\mathfrak {su}(1,1))\) Symmetry

By using the algebraic construction outlined in Carinci et al. (arXiv:1407.3367, 2014), we introduce several Markov processes related to the

Free Boundary Problems in PDEs and Particle Systems

{\mathscr {U}}_q(\mathfrak {su}(1,1))

Quantitative Boltzmann–Gibbs Principles via Orthogonal Polynomial Duality

Uq(su(1,1)) quantum Lie algebra. These processes serve as asymmetric transport models and their algebraic structure easily allows to deduce duality properties of the systems. The results include: (a) the asymmetric version of the Inclusion Process, which is self-dual; (b) the diffusion limit of this process, which is a natural asymmetric analogue of the and which turns out to have the Symmetric Inclusion Process as a dual process; (c) the asymmetric analogue of the KMP Process, which also turns out to have a symmetric dual process. We give applications of the various duality relations by computing exponential moments of the current.

Mass Transport Inequalities

By using the algebraic construction outlined in Carinci et al. (arXiv:1407.3367, 2014), we introduce several Markov processes related to the

Existence of Optimal Sequences

{\mathscr {U}}_q(\mathfrak {su}(1,1))