Functional Central Limit Theorem for the simultaneous subgraph count of dynamic Erdős-Rényi random graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912731432484864 |
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| author | Hazra, Rajat Subhra Kriukov, Nikolai Mandjes, Michel |
| author_facet | Hazra, Rajat Subhra Kriukov, Nikolai Mandjes, Michel |
| contents | In this paper we consider a dynamic Erdős-Rényi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this paper is a functional central limit theorem: we establish, under an appropriate centering and scaling, the joint functional convergence of the vector of subgraph counts to a specific multidimensional Gaussian process. The result holds under mild assumptions on the edge processes, most notably a Lipschitz-type condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional Central Limit Theorem for the simultaneous subgraph count of dynamic Erdős-Rényi random graphs Hazra, Rajat Subhra Kriukov, Nikolai Mandjes, Michel Probability Combinatorics In this paper we consider a dynamic Erdős-Rényi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this paper is a functional central limit theorem: we establish, under an appropriate centering and scaling, the joint functional convergence of the vector of subgraph counts to a specific multidimensional Gaussian process. The result holds under mild assumptions on the edge processes, most notably a Lipschitz-type condition. |
| title | Functional Central Limit Theorem for the simultaneous subgraph count of dynamic Erdős-Rényi random graphs |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2502.01259 |