Stochastic interacting particle systems and nonlinear kinetic equations

Field theories and exact stochastic equations for interacting particle systems.

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further th...

Interacting particle systems as stochastic social dynamics

The style of mathematical models known to probabilists as Interacting Particle Systems and exemplified by the Voter, Exclusion and Contact processes have found use in many academic disciplines. In many such disciplines the underlying conceptual picture is of a social network, where individuals meet pairwise and update their “state” (opinion, activity etc) in a way depending on the two previous ...

Nonlinear Fluctuations of Interacting Particle Systems

We introduce what we call the second-order Boltzmann-Gibbs principle, which allows to replace local functionals of a conservative, onedimensional stochastic process by a possibly nonlinear function of the conserved quantity. This replacement opens the way to obtain nonlinear stochastic evolutions as the limit of the fluctuations of the conserved quantity around stationary states. As an applicat...

Particle Systems and Kinetic Equations Modeling Interacting Agents in High Dimension

In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such systems, one has to deal with a large number of agents (typically millions) in spaces of parameters describing each agent of high dimension (thousands or more). ...

Kinetic Equations for Quantum Many-Particle Systems