Kiran R. Bhutani ; Ravi Kalpathy ; Hosam Mahmoud - Degrees in random $m$-ary hooking networks

compositionality:13525 - Compositionality, August 9, 2023, Volume 5 (2023) - https://doi.org/10.32408/compositionality-5-6
Degrees in random $m$-ary hooking networksArticle

Authors: Kiran R. Bhutani 1; Ravi Kalpathy ORCID1; Hosam Mahmoud 2

  • 1 Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, U.S.A.
  • 2 Department of Statistics, The George Washington University, Washington, D.C. 20052, U.S.A.

The theme in this paper is a composition of random graphs and Pólya urns. The random graphs are generated through a small structure called the seed. Via Pólya urns, we study the asymptotic degree structure in a random $m$-ary hooking network and identify strong laws. We further upgrade the result to second-order asymptotics in the form of multivariate Gaussian limit laws. We give a few concrete examples and explore some properties with a full representation of the Gaussian limit in each case. The asymptotic covariance matrix associated with the Pólya urn is obtained by a new method that originated in this paper and is reported in [25].


Volume: Volume 5 (2023)
Published on: August 9, 2023
Imported on: May 2, 2024
Keywords: Mathematics - Probability,05C82, 90B15 (Primary) 60C05, 60F05 (Secondary)

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