Young Researchers Seminars, Maths Applications & Models (Fraccarolo, Marini)

Nicola Fraccarolo (Università di Trento)
Finite State Graphon Mean Field Games

In this joint work with Francesco Giuseppe Cordoni (University of Trento, Italy) and Luca Di Persio (University of Verona, Italy) we will talk about stochastic games on large graphs, where the players no longer interact with each other symmetrically. To encode this information, the concept of graphon is employed. Graphons are the natural continuum limits for dense interaction matrices. Matematically, a graphon is a symmetric measurable function $W: [0, 1]^2 \to [0,1]$, with $W(u, v)$ representing the interaction between vertices players $u$ and $v$. We consider a continuous-time controlled dynamics on finite states: we write the dynamics of the $N$-player game as a system of stochastic differential equations driven by independent stationary Poisson random measures. Under a set of fairly general assumptions, we derive the existence of both relaxed and non-relaxed controls, while uniqueness is proven under the Lasry-Lions monotonicity conditions.

Elisa Marini (Università di Padova)
Noise-induced oscillations for the mean-field Dissipative Contact Process

In this talk, we will introduce a dissipative version of the contact process with mean-field interaction admitting a simple epidemiological interpretation. In particular, we will focus on the thermodynamic limit of the process, providing a law of large numbers (propagation of chaos) and a central limit theorem for the corresponding normal fluctuations. These results reveal that it is the noise, which is only present in the finite-size system and is internal to the system, that induces persistent oscillatory behaviors reminiscent of the emergence of pandemic waves in real epidemics.

Further information at this link