Rangel Baldasso (Bar-Ilan University, Israel)
Title: Spread of an infection on the zero range process
Abstract: We consider the spread of an infection on top of a moving population. The environment evolves as a zero range process on the integer lattice starting in equilibrium. At time zero, the set of infected particles is composed by those which are on the negative axis, while particles at the right of the origin are considered healthy. A healthy particle immediately becomes infected if it shares a site with an infected particle. We prove that the front of the infection wave travels to the right with positive and finite velocity.
Renato De Paula (IST Lisbon, Portugal)
Title: Porous medium model in contact with slow reservoirs.
Abstract: The porous medium model is an interacting particle system which belongs to the class of Kinetically constrained lattice gases (KCLG). In this poster, we are interested in studying the hydrodynamic limit of this model in contact with slow reservoirs, which guarantees that the evolution of the density of particles of this model is described by the weak solution of the corresponding hydrodynamic equation, namely, the porous medium equation with Dirichlet, Neumann and Robin boundary conditions, depending on the parameter that rules the slowness of the reservoirs.
Marina Ferreira (Helsinki University, Finland)
Title: Coagulation systems for aerosol dynamics
Abstract: Over one day experimentally, particles grow by colliding and merging with other particles until the size distribution stabilizes in some region of the size space. We start by considering a discrete coagulation model to describe the dynamics of the particle-size distribution. We then study well-posedness of time-dependent solutions and discuss the existence of steady states. In order to understand the effect of the chemical composition of particles, we further consider a multi-component coagulation system. We investigate the interesting and relatively generic phenomenon in which the mass concentrates along straight lines in the particle-size space for large times. Finally, we discuss possible modeling improvements by adding source, sink and fragmentation terms.
Chiara Franceschini (University of Modena, Italy)
Title: An algebraic approach to stochastic duality.
Abstract: Duality in the context of stochastic processes is a powerful tool to deal with interacting particle systems (IPS) and diffusion processes.
Besides a wide range of applications (population genetics, scaling limits, transport models...) it is interesting to understand the mathematical structure behind duality which is deeply connected with Lie algebras and their representation. For a class of IPS, we show a constructive technique to build self-duality relations based on symmetries of their generators, in particular, we establish the unitary symmetry which produces the family of orthogonal polynomials which are self-duality functions.
Rodrigo Marinho (IST Lisbon, Portugal)
Title: Abrupt convergence to equilibrium of the exclusion process.
Abstract: The simple exclusion process is a model used to describe the relaxation of a low-density gas. Its hydrodynamic limits have been studied by many people and, recently, Lacoin used the hydrodynamic equations to prove that the system mixes at time $\Theta{(n^2\log{n})}$, exhibiting the correct constant factor for circles, paths and complete graphs. We attack the problem with a different approach. We use Yau's relative entropy method to show that, after sufficiently large time, the distance to equilibrium of the system is close to a function which we use to determine the mixing time. We consider the simple symmetric exclusion process on the path in contact with reservoirs at density $1/2$ and show that it presents cutoff at time $\frac{1}{8/pi^2}n^2\log{n}$ with a window of size $n^2$. The addition of reservoirs shows how powerful the method is since it destroys most of the combinatoric strategies used before.
Otávio Menezes (IST Lisbon, Portugal)
Title: Non-equilibrium fluctuations of interacting particle systems.
Abstract: We obtain the large-scale limit of the fluctuations around its hydrodynamic limit of the density of particles of two particle systems: a weakly asymmetric exclusion process in dimensions 3 or smaller and a reaction-diffusion process in dimension 1. The proof is based upon a sharp estimate on the relative entropy of the law of the process with respect to product reference measures associated to the hydrodynamic limit profile, which holds in any dimension and is of independent interest. Joint work with Milton Jara.
Frederico Sau (Delft University, Netherlands)
Title: Symmetric simple exclusion process in dynamic environment: hydrodynamics
Abstract: For the simple exclusion process evolving in a symmetric dynamic random environment, we derive the hydrodynamic limit from the quenched invariance principle of the corresponding random walk. For instance, if the limiting behavior of a test particle resembles that of Brownian motion on a diffusive scale, the empirical density, in the limit and suitably rescaled, evolves according to the heat equation.
Our goal is to make this connection explicit for the simple exclusion process and show how self-duality of the process enters the problem. This allows us to extend the result to other conservative particle systems (e.g. IRW, SIP) which share a similar property.
Joint work with F. Redig and E. Saada.
Stefano Scotta (IST Lisbon, Portugal)
Title: Equilibrium fluctuations for the symmetric exclusion with long jumps
Abstract: The goal of this poster is to show that it is possible to describe the fluctuations around the equilibrium for an exclusion process with long jumps and infinitely extended reservoirs, using a stochastic partial differential equation, whose solution is known in the literature as the generalized Ornstein-Uhlenbeck process.