The Four Levels of Fixed-Points in Mean-Field Models
Abstract
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle systems. These four levels are (i) the macroscopic observables of the system, (ii) the probability distribution over states of a particle at equilibrium, (iii) the time evolution of the probability distribution over states of a particle, and (iv) the probability distribution over trajectories. We then discuss relationships among the fixed-points at these four levels. Finally, we describe some issues that arise in the fixed-point analysis when the system possesses multiple fixed-points at the level of distribution over states, and how one goes beyond the fixed-point analysis to tackle such issues.
Keywords
Cite
@article{arxiv.2106.02807,
title = {The Four Levels of Fixed-Points in Mean-Field Models},
author = {Sarath Yasodharan and Rajesh Sundaresan},
journal= {arXiv preprint arXiv:2106.02807},
year = {2021}
}
Comments
Accepted for publication at the Twenty Seventh National Conference on Communications (NCC 2021)