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Preprint
The Large Deviation Principle for W-random spectral measures
ArXiv.org
07 May 2024
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
[9], 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 the
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 underlying graphons and use the Contraction
Principle. To illustrate our results, we obtain leading order asymptotics of
the eigenvalues of the integral operators corresponding to certain random graph
sequences. These examples suggest several representative scenarios of how the
eigenvalues and the eigenspaces of the integral operators are affected by large
deviations. Potential implications of these observations for bifurcation
analysis of Dynamical Systems and Graph Signal Processing are indicated.
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Details
- Title
- The Large Deviation Principle for W-random spectral measures
- Creators
- Mahya GhandehariGeorgi S Medvedev
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021874415604721