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Local limit of the random degree constrained process
- Publication Year :
- 2024
-
Abstract
- 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 $d$.<br />Comment: 53 pages, 3 figures
- Subjects :
- Mathematics - Probability
05C80, 60C05, 60J80
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.11747
- Document Type :
- Working Paper