Scale-free percolation mixing time

Scale-free percolation mixing time

Cipriani, A. (TU Delft Applied Probability)
Salvi, Michele (University of Rome Tor Vergata)

2024

Assign to each vertex of the one-dimensional torus i.i.d. weights with a heavy-tail of index τ−1>0. Connect then each couple of vertices with probability roughly proportional to the product of their weights and that decays polynomially with exponent α>0 in their distance. The resulting graph is called scale-free percolation. The goal of this work is to study the mixing time of the simple random walk on this structure. We depict a rich phase diagram in α and τ. In particular we prove that the presence of hubs can speed up the mixing of the chain. We use different techniques for each phase, the most interesting of which is a bootstrap procedure to reduce the model from a phase where the degrees have bounded averages to a setting with unbounded averages.

Degree distribution
Mixing time
Random graph
Scale-free percolation

http://resolver.tudelft.nl/uuid:1f60409e-4439-45be-ace1-1a9bc05a1812

https://doi.org/10.1016/j.spa.2023.104236

2024-04-29

0304-4149

Stochastic Processes and their Applications, 167

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2024 A. Cipriani, Michele Salvi