Degrees in random $m$-ary hooking networks
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929450024697856 |
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| author | Bhutani, Kiran R. Kalpathy, Ravi Mahmoud, Hosam |
| author_facet | Bhutani, Kiran R. Kalpathy, Ravi Mahmoud, Hosam |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03857 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Degrees in random $m$-ary hooking networks Bhutani, Kiran R. Kalpathy, Ravi Mahmoud, Hosam Probability 05C82, 90B15 (Primary) 60C05, 60F05 (Secondary) 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]. |
| title | Degrees in random $m$-ary hooking networks |
| topic | Probability 05C82, 90B15 (Primary) 60C05, 60F05 (Secondary) |
| url | https://arxiv.org/abs/2308.03857 |