Asymptotic behavior and distributional limits of preferential attachment graphs

By Noam Berger, Christian Borgs, Jennifer Tour Chayes, Amin Saberi. 2014

111 citations recorded by the source corpus.

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree distributions and, more generally, the limiting distribution of subgraphs in balls of any given radius $k$ around a random vertex in the preferential attachment graph. We also establish the finite-volume corrections which give the approach to the limit.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b36d493d764e46df86a378dae0e1a33a2df1fe41

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Jean-Christophe Mourrat
2. Balázs Szegedy
3. Felix Otto
4. Antoine Gloria
5. Stefan Neukamm
6. S. Armstrong

In Statistical and Nonlinear Physics

1. Jean-Christophe Mourrat
2. Daniel Valesin
3. Qiang Yao
4. Thomas Mountford

In Statistics and Probability

1. Jean-Christophe Mourrat
2. Felix Otto
3. Antoine Gloria
4. Stefan Neukamm

Citations in the corpus

• Exponential extinction time of the contact process on finite graphs (2012, background): “It would be interesting to investigate whether the results presented here (possibly in combination with the recent [3]) enable to show that the extinction time is actually of the order of exp(cn) for some constant c.”
• Action convergence of operators and graphs (2018, background): “They converge in the Benjamini–Schramm metric [5, 34], moreover they are trees and thus they are hyperfinite graphs.”