Local limit of the random degree constrained process
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908705112457216 |
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| author | Ráth, Balázs Szőke, Márton Warnke, Lutz |
| author_facet | Ráth, Balázs Szőke, Márton Warnke, Lutz |
| contents | In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover, identify the limit object as a multi-type branching process, by combining coupling arguments with the analysis of a certain recursive tree process. Using a spectral characterization, we also give an asymptotic expansion of the critical time when the giant component emerges in the so-called random $d$-process, resolving a problem of Warnke and Wormald for large $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local limit of the random degree constrained process Ráth, Balázs Szőke, Márton Warnke, Lutz Probability 05C80, 60C05, 60J80 In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover, identify the limit object as a multi-type branching process, by combining coupling arguments with the analysis of a certain recursive tree process. Using a spectral characterization, we also give an asymptotic expansion of the critical time when the giant component emerges in the so-called random $d$-process, resolving a problem of Warnke and Wormald for large $d$. |
| title | Local limit of the random degree constrained process |
| topic | Probability 05C80, 60C05, 60J80 |
| url | https://arxiv.org/abs/2409.11747 |