# PRIN 2022 :

# "Emergence of condensation-like phenomena

# in interacting particle systems:

# kinetic and lattice models."

Research Units:

Università degli Studi di Modena e Reggio Emilia

Gioia Carinci (Co-P.I.)

Cristian Giardinà

Claudio Giberti

Università degli Studi di Roma "La Sapienza"

Giada Basile (Co-P.I.)

Dario Benedetto

Stefano Marchesani

Brief description of the project

Condensation is a widespread phenomenon in nature where a macroscopic fraction of an observed quantity concentrates in a single state, typically when some specific parameter of the model crosses a critical threshold. It represents a special phase transition which exhibits concentration and clustering. Classical examples of problems that can be thought as condensation are the Bose-Einstein condensation, gelation in polymers, vapor condensation of gas molecules on aerosol in atmosphere, formation of traffic jams. These phenomena typically emerge in the context of different complex systems, constituted by a very large number of components. Nonetheless, condensation processes can be well described by simple mathematical models which in the large scale limit retain the essential features.

The main purpose of this project is to investigate the emergence of concentration and condensation in interacting particle systems. More precisely, we will focus on binary collisions kinetic models and stochastic lattice dynamics. Condensation will then appear in the limit of large number of particles, under suitable rescaling. We aim to study the phenomenon both as typical behavior (i.e. at the level of the law of large numbers) and at the level of large deviations.

Research Lines

This project draws the following two research lines

Kinetic models of condensation-like phenomena

Lattice models of condensation-like phenomena

aiming at solving some specific objectives which represent relevant problems in non-equilibrium statistical mechanics.