On the effect of heterogeneity in stochastic interacting-particle systems

Methods and ideas developed in statistical physics are being transferred to other disciplines, such as ecology, epidemiology, sociology, economy, etc., focusing on collective and emergent phenomena in what is known as complexity science. Unlike the systems traditionally studied by physics, which consist of identical (some times even indistinguishable) units (molecules, atoms, electrons), the new applications require the consideration of systems which are characterized by a large degree of heterogeneity among their constituent units. Furthermore, very often these systems can be modeled only at a stochastic level, since a complete knowledge of all the variables, the precise dynamics of the units and the interaction with the environment is not available.

In this talk, we will consider stochastic particle systems made up of heterogeneous units. We will introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We will show that particle heterogeneity can enhance or decrease the collective fluctuations depending on the system, and that it is possible to infer the degree and the form of the heterogeneity distribution in the system by measuring only global variables and their fluctuations.