Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model
We propose an algorithm for the closed-form recursive computation of joint moments and cumulants of all orders of k-hop counts in the 1D unit disk random graph model with Poisson distributed vertices. Our approach uses decompositions of k-hop counts into multiple Poisson stochastic integrals. As a c...
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| Format: | Journal Article |
| Language: | English |
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2025
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| Online Access: | https://hdl.handle.net/10356/181960 |
| _version_ | 1826125426163974144 |
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| author | Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Privault, Nicolas |
| author_sort | Privault, Nicolas |
| collection | NTU |
| description | We propose an algorithm for the closed-form recursive computation of joint moments and cumulants of all orders of k-hop counts in the 1D unit disk random graph model with Poisson distributed vertices. Our approach uses decompositions of k-hop counts into multiple Poisson stochastic integrals. As a consequence, using the Stein and cumulant methods we derive Berry-Esseen bounds for the asymptotic convergence of renormalized k-hop path counts to the normal distribution as the density of Poisson vertices tends to infinity. Computer codes for the recursive symbolic computation of moments and cumulants of any orders are provided as an online resource. |
| first_indexed | 2025-03-09T14:01:57Z |
| format | Journal Article |
| id | ntu-10356/181960 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-03-09T14:01:57Z |
| publishDate | 2025 |
| record_format | dspace |
| spelling | ntu-10356/1819602025-01-06T15:35:22Z Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model Privault, Nicolas School of Physical and Mathematical Sciences Mathematical Sciences Random graph 1D unit disk model We propose an algorithm for the closed-form recursive computation of joint moments and cumulants of all orders of k-hop counts in the 1D unit disk random graph model with Poisson distributed vertices. Our approach uses decompositions of k-hop counts into multiple Poisson stochastic integrals. As a consequence, using the Stein and cumulant methods we derive Berry-Esseen bounds for the asymptotic convergence of renormalized k-hop path counts to the normal distribution as the density of Poisson vertices tends to infinity. Computer codes for the recursive symbolic computation of moments and cumulants of any orders are provided as an online resource. Ministry of Education (MOE) Submitted/Accepted version This research is supported by the Ministry of Education, Singapore, under its Tier 1 Grant RG103/23. 2025-01-04T08:07:43Z 2025-01-04T08:07:43Z 2024 Journal Article Privault, N. (2024). Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model. Methodology and Computing in Applied Probability, 26(4), 47-. https://dx.doi.org/10.1007/s11009-024-10115-9 1387-5841 https://hdl.handle.net/10356/181960 10.1007/s11009-024-10115-9 2-s2.0-85207020539 4 26 47 en RG103/23 Methodology and Computing in Applied Probability © 2024 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1007/s11009-024-10115-9. application/pdf |
| spellingShingle | Mathematical Sciences Random graph 1D unit disk model Privault, Nicolas Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model |
| title | Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model |
| title_full | Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model |
| title_fullStr | Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model |
| title_full_unstemmed | Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model |
| title_short | Asymptotic analysis of k-hop connectivity in the 1D unit disk random graph model |
| title_sort | asymptotic analysis of k hop connectivity in the 1d unit disk random graph model |
| topic | Mathematical Sciences Random graph 1D unit disk model |
| url | https://hdl.handle.net/10356/181960 |
| work_keys_str_mv | AT privaultnicolas asymptoticanalysisofkhopconnectivityinthe1dunitdiskrandomgraphmodel |