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April 2020 Nonlinear large deviations: Beyond the hypercube
Jun Yan
Ann. Appl. Probab. 30(2): 812-846 (April 2020). DOI: 10.1214/19-AAP1516

Abstract

By extending (Adv. Math. 299 (2016) 396–450), we present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces. Previous research on nonlinear large deviations has only focused on random variables supported on $\{-1,+1\}^{n}$, and accordingly we build theory for random variables with general distributions, increasing flexibility in the applications. As examples, we compute the large deviation rate functions for monochromatic subgraph counts in edge-colored complete graphs, and for triangle counts in dense random graphs with continuous edge weights. Moreover, we verify the mean field approximation for a class of vector spin models.

Citation

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Jun Yan. "Nonlinear large deviations: Beyond the hypercube." Ann. Appl. Probab. 30 (2) 812 - 846, April 2020. https://doi.org/10.1214/19-AAP1516

Information

Received: 1 July 2018; Revised: 1 March 2019; Published: April 2020
First available in Project Euclid: 8 June 2020

zbMATH: 07236135
MathSciNet: MR4108123
Digital Object Identifier: 10.1214/19-AAP1516

Subjects:
Primary: 05C80, 60C05, 60F10, 60K35

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 2 • April 2020
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