### Abstract

Original language | English |
---|---|

Pages (from-to) | 808-830 |

Number of pages | 23 |

Journal | Random Structures and Algorithms |

Volume | 55 |

Issue number | 4 |

Early online date | 2 Apr 2019 |

DOIs | |

Publication status | Published - 1 Dec 2019 |

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### Keywords

- random graphs
- Preferential attachment
- Stein's method
- coupling
- rates of convergence

### Cite this

*Random Structures and Algorithms*,

*55*(4), 808-830. https://doi.org/10.1002/rsa.20852

**Fluctuations in a general preferential attachment model via Stein's method.** / Betken, Carina; Döring, Hanna; Ortgiese, Marcel.

Research output: Contribution to journal › Article

*Random Structures and Algorithms*, vol. 55, no. 4, pp. 808-830. https://doi.org/10.1002/rsa.20852

}

TY - JOUR

T1 - Fluctuations in a general preferential attachment model via Stein's method

AU - Betken, Carina

AU - Döring, Hanna

AU - Ortgiese, Marcel

PY - 2019/12/1

Y1 - 2019/12/1

N2 - We consider a class of dynamic random graphs known as preferential attachment models, where the probability that a new vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known that the distribution of a uniformly chosen vertex converges to a limiting distribution. Depending on the parameters, the tail of the limiting distribution may behave like a power law or a stretched exponential. Using Stein's method we provide rates of convergence to zero of the total variation distance between the finite distribution and its limit. Our proof uses the fact that the limiting distribution is the stationary distribution of a Markov chain together with the generator method of Barbour.

AB - We consider a class of dynamic random graphs known as preferential attachment models, where the probability that a new vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known that the distribution of a uniformly chosen vertex converges to a limiting distribution. Depending on the parameters, the tail of the limiting distribution may behave like a power law or a stretched exponential. Using Stein's method we provide rates of convergence to zero of the total variation distance between the finite distribution and its limit. Our proof uses the fact that the limiting distribution is the stationary distribution of a Markov chain together with the generator method of Barbour.

KW - random graphs

KW - Preferential attachment

KW - Stein's method

KW - coupling

KW - rates of convergence

U2 - 10.1002/rsa.20852

DO - 10.1002/rsa.20852

M3 - Article

VL - 55

SP - 808

EP - 830

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 4

ER -