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Monochromatic Subgraphs in Multiplex Networks Mauricio Daros Andrade
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Daros Andrade, Mauricio, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Statistics.
- Theoretical mathematics.
- Computer science.
- Information science.
- 0405.
- 0463.
- 0642.
- 0984.
- 0723.
- Local Subjects:
- Mathematics.
- Statistics.
- Theoretical mathematics.
- Computer science.
- Information science.
- 0405.
- 0463.
- 0642.
- 0984.
- 0723.
- Physical Description:
- 1 electronic resource (90 pages)
- Contained In:
- Dissertations Abstracts International 86-12A
- Place of Publication:
- Ann Arbor : ProQuest Dissertations and Theses, 2025
- Language Note:
- English
- Summary:
- Given a sequence of graphs {Gn}n≥1 and fixed graph H, denote by T(H, Gn) the number of monochromatic copies of the graph H in Gn in a uniformly random cn-coloring of the vertices of Gn. In this dissertation we study the joint distribution of monochromatic subgraphs for dense multiplex networks, that is, networks with multiple layers. Specifically, given a finite collection of graphs H1, . . . , Hd, we derive the asymptotic joint distribution of Tn := (T(H1, G(1)n ), . . . , T(Hd, G(d)n )), where Gn = (G(1)n , . . . , G(d)n ) is a collection of graphs on the same vertex set converging in the joint cut-metric.Under a notion of joint convergence of Gn in the cut metric, we show that when the number of colors cn = c is fixed, then the limiting distribution of Tn is the sum of two independent components, one of which is a multivariate Gaussian and the other is a sum of bivariate stochastic integrals. On the other hand, when the number of colors cn → ∞ (such that \uD835\uDD3C[Tn] → ∞), then the asymptotic distribution of Tn is a multivariate normal. This generalizes the classical birthday problem, which involves understanding the asymptotics of T(Ks, Kn), the number of monochromatic s-cliques in a complete graph Kn (s-matching birthdays among a group of n friends), to general monochromatic subgraphs in multiplex networks. This also extends previous results on the marginal convergence of T(H, Gn) and is useful in establishing the joint convergence of various subgraph counting statistics that arise from random vertex coloring of graphs. Several applications and examples are discussed
- Notes:
- Source: Dissertations Abstracts International, Volume: 86-12, Section: A.
- Advisors: Bhattacharya, Bhaswar B. Committee members: Huang, Jiaoyang; Low, Mark G.
- Ph.D. University of Pennsylvania 2025
- Local Notes:
- School code: 0175
- ISBN:
- 9798280757974
- Access Restriction:
- Restricted for use by site license
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