##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics

## Márton Szőke

#### Budapest University of Technology

## Local Limit of the Random Degree Constrained Process

##### Abstract:

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 $d$.

Based on joint work with Balázs Ráth and Lutz Warnke; see arXiv:2409.11747

Lutz Warnke

### October 31, 2024

### 11:00 AM

APM 6402

(**Zoom-Talk**: Meeting ID: 980 5804 6945, Password: 271781)

Research Areas

Combinatorics Probability Theory****************************