The four levels of fixed-points in mean-field models

Yasodharan, S and Sundaresan, R (2021) The four levels of fixed-points in mean-field models. In: 27th National Conference on Communications, NCC 2021, 27-30 Jul 2021, Kanpur.

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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. © 2021 IEEE.

Item Type:	Conference Paper
Publication:	2021 National Conference on Communications, NCC 2021
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Mean field theory; Vlasov equation, A-particles; Fixed point analysis; Fixed points; Interacting particle system; McKean-Vlasov equations; Mean field limits; Mean field models; Performances analysis; Probability: distributions; Propagation of chaos, Probability distributions
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	07 Dec 2021 10:22
Last Modified:	07 Dec 2021 10:22
URI:	http://eprints.iisc.ac.in/id/eprint/70378

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