Particle Systems and Kinetic Equations Modeling Interacting Agents in High Dimension

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

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...

Learning interacting particle systems: diffusion parameter estimation for aggregation equations

In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation. Specifically, we construct an estimator ν̂ with partial observed data to approximate the diffusion parameter ν, and the estimation error is achieved. Furthermore, we extend this result to general aggregation equations with a bounded Lipschitz interaction field.

Reaction-Diffusion Equations for Interacting Particle Systems I

We study interacting spin (particle) systems on a lattice under the combined influence of spin flip (Glauber) and simple exchange (Kawasaki) dynamics. We prove that when the particle-conserving exchanges (stirrings) occur on a fast time scale of order ~-2 the macroscopic density, defined on spatial scale e -~, evolves according to an autonomous nonlinear diffusion-reaction equation. Microscopic...