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Concentration of measure for graphon particle system

Part of: Graph theory Markov processes Special processes

Published online by Cambridge University Press:  19 January 2024

Erhan Bayraktar Open the ORCID record for Erhan Bayraktar [Opens in a new window]  and
Donghan Kim
Erhan Bayraktar*
Affiliation:
University of Michigan
Donghan Kim*
Affiliation:
University of Michigan
*
*Postal address: Department of Mathematics, 530 Church Street, Ann Arbor, MI 48109.
**Email address: erhan@umich.edu
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Abstract

We study heterogeneously interacting diffusive particle systems with mean-field-type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration estimates over a finite time horizon for both 1- and 2-Wasserstein distances between the empirical measures of the finite particle systems and the averaged law of the graphon system.

Keywords

Mean-field interactionheterogeneous interactionnetworksconcentration boundstransportation inequalitiesL1-Fourier class

MSC classification

Primary: 60J60: Diffusion processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 05C80: Random graphs
Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 28
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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