Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials

Generalizing previous work of Hora (1998) on the asymptotic spectral analysis for the Hamming graph H(n, q) which is the nth Cartesian power Kq□n of the complete graph Kq on q vertices, we describe the possible limits of the joint spectral distribution of the pair (G□n, G□n) of the nth Cartesian pow...

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Main Authors: Morales, John Vincent S., Obata, Nobuaki, Tanaka, Hajime
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Published: Animo Repository 2018
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Online Access:https://animorepository.dlsu.edu.ph/faculty_research/5940
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Institution: De La Salle University
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spelling oai:animorepository.dlsu.edu.ph:faculty_research-68782022-06-01T00:14:44Z Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials Morales, John Vincent S. Obata, Nobuaki Tanaka, Hajime Generalizing previous work of Hora (1998) on the asymptotic spectral analysis for the Hamming graph H(n, q) which is the nth Cartesian power Kq□n of the complete graph Kq on q vertices, we describe the possible limits of the joint spectral distribution of the pair (G□n, G□n) of the nth Cartesian powers of a strongly regular graph G and its complement G, where we let n → ∞, and G may vary with n. This result is an analogue of the bivariate central limit theorem, and we obtain in this way the bivariate Poisson distributions and the standard bivariate Gaussian distribution, together with the product measures of univariate Poisson and Gaussian distributions. We also report a family of bivariate hypergeometric orthogonal polynomials with respect to the last distributions, which we call the bivariate Charlier–Hermite polynomials, and prove basic formulas for them. This family of orthogonal polynomials seems previously unnoticed, possibly because of its peculiarity. 2018-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/5940 Faculty Research Work Animo Repository Graph theory Hypergeometric series Orthogonal polynomials Hilbert space Central limit theorem Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
topic Graph theory
Hypergeometric series
Orthogonal polynomials
Hilbert space
Central limit theorem
Mathematics
spellingShingle Graph theory
Hypergeometric series
Orthogonal polynomials
Hilbert space
Central limit theorem
Mathematics
Morales, John Vincent S.
Obata, Nobuaki
Tanaka, Hajime
Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials
description Generalizing previous work of Hora (1998) on the asymptotic spectral analysis for the Hamming graph H(n, q) which is the nth Cartesian power Kq□n of the complete graph Kq on q vertices, we describe the possible limits of the joint spectral distribution of the pair (G□n, G□n) of the nth Cartesian powers of a strongly regular graph G and its complement G, where we let n → ∞, and G may vary with n. This result is an analogue of the bivariate central limit theorem, and we obtain in this way the bivariate Poisson distributions and the standard bivariate Gaussian distribution, together with the product measures of univariate Poisson and Gaussian distributions. We also report a family of bivariate hypergeometric orthogonal polynomials with respect to the last distributions, which we call the bivariate Charlier–Hermite polynomials, and prove basic formulas for them. This family of orthogonal polynomials seems previously unnoticed, possibly because of its peculiarity.
format text
author Morales, John Vincent S.
Obata, Nobuaki
Tanaka, Hajime
author_facet Morales, John Vincent S.
Obata, Nobuaki
Tanaka, Hajime
author_sort Morales, John Vincent S.
title Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials
title_short Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials
title_full Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials
title_fullStr Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials
title_full_unstemmed Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials
title_sort asymptotic joint spectra of cartesian powers of strongly regular graphs and bivariate charlier–hermite polynomials
publisher Animo Repository
publishDate 2018
url https://animorepository.dlsu.edu.ph/faculty_research/5940
_version_ 1794553705915219968