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The Large Deviation Principle for W-random spectral measures
Journal article   Open access   Peer reviewed

The Large Deviation Principle for W-random spectral measures

Mahya Ghandehari and Georgi S. Medvedev
Applied and computational harmonic analysis, v 77, 101756
Jun 2025
url
https://arxiv.org/abs/2405.04417View

Abstract

eigenvalue graph limit large deviations random graph spectral measure
The W-random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for W-random graphs from [19], we prove the LDP for the corresponding class of random symmetric Hilbert-Schmidt integral operators. Our main result describes how the eigenvalues and the eigenspaces of the integral operator are affected by large deviations in the underlying random graphon. To prove the LDP, we demonstrate continuous dependence of the spectral measures associated with integral operators on the corresponding graphons and use the Contraction Principle. To illustrate our results, we obtain leading order asymptotics of the eigenvalues of small-world and bipartite random graphs conditioned on atypical edge counts. These examples suggest several representative scenarios of how the eigenvalues and the eigenspaces are affected by large deviations. We discuss the implications of these observations for bifurcation analysis of Dynamical Systems and Graph Signal Processing.

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Collaboration types
Domestic collaboration
Web of Science research areas
Mathematics, Applied
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