EF45 – Multi-Agent Complex Systems

Project

EF45-5

A New Approach to Metastability in Multi-Agent Systems

Project Heads

Maximilian Engel

Project Members

Zachary P. Adams

Project Duration

01.02.2024 – 31.12.2025

Located at

FU Berlin

Description

Motivated by challenges in biology, the social sciences, and opinion dynamics, we consider large systems of SDEs, modeling the dynamics of interacting entities.  We aim to describe and quantify phenomena of fast attraction to certain clusters followed by slow leakage due to diffusion, making use of sub-Markovian semigroups, quasi-stationary distributions, and associated spectral methods.
In the course of our studies, we contribute to the development of a general theory for the characterization of metastable features and the time-scales on which they are observed.  We also apply this general theory to the novel problem of statistical inference of time-series which appear to exhibit several metastable regimes, such as those observed in time series generated by multi-agent systems.

Selected Publications

  1. Adams ZP, MacLaurin J. The isochronal phase of stochastic PDE and integral equations: Metastability and other properties. Journal of Differential Equations. 2025; 414: 773-816.
  2. Adams ZP. Quasi-Ergodicity of transient patterns in stochastic reaction-diffusion equations. Electronic Journal of Probability. 2024;29:1-29.
  3. Adams ZP. Existence, regularity, and a strong Itô formula for the isochronal phase of SPDE. Electronic Communications in Probability. 2024;29:1-2.
  4. Adams ZP, Mukherjee S. Meta-posterior consistency for the Bayesian inference of metastable systems. arXiv preprint arXiv:2408.01868. 2024.
  5. Venegas-Pineda LG, Jardón-Kojakhmetov H, Engel M, Heitzig J, Eser MC, Cao M. Strategic control for a Boltzmann like decision-making model. arXiv preprint arXiv:2405.10915. 2024 May 17.

Selected Pictures

Schematic depicting metastability. A trajectory starting at μ rapidly converges to a manifold M of metastable states. The trajectory exhibits slow motion on this manifold. In the systems we study, trajectories eventually leave the vicinity of the manifold due to stochastic forcing.

Dynamical metastability in a system of weakly interacting particles.  Each curve represents the distribution of the system of particles at a different point in time, as indicated by the color bar on the right.  In this figure, we observe the rapid convergence of the system of particles to a metastable “droplet state”.  On much longer timescales, the droplet state disperses, and the distribution of the particles tends to zero at each point on the real line.