Journal article
The Large Deviation Principle for W-random spectral measures
Applied and computational harmonic analysis, v 77, 101756
Jun 2025
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
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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Details
- Title
- The Large Deviation Principle for W-random spectral measures
- Creators
- Mahya Ghandehari - University of DelawareGeorgi S. Medvedev - Drexel University, Mathematics
- Publication Details
- Applied and computational harmonic analysis, v 77, 101756
- Publisher
- Elsevier
- Number of pages
- 12
- Grant note
- National Science Foundation: DMS-1902301, DMS-2408008, DMS-2009233, DMS-2406941
This work was partially supported by the National Science Foundation Grants DMS-1902301, DMS-2408008 (to MG) and DMS-2009233, DMS-2406941 (to GM) .
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001433396100001
- Scopus ID
- 2-s2.0-85218354096
- Other Identifier
- 991022032172004721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied