Cipriani, Alessandra;
Salvi, Michele;
(2024)
Scale-free percolation mixing time.
Stochastic Processes and their Applications
, 167
, Article 104236. 10.1016/j.spa.2023.104236.
(In press).
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Abstract
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 scalefree 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.
| Type: | Article |
|---|---|
| Title: | Scale-free percolation mixing time |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.spa.2023.104236 |
| Publisher version: | https://doi.org/10.1016/j.spa.2023.104236 |
| Language: | English |
| Additional information: | https://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Random graph; Mixing time; Scale-free percolation; Degree distribution |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10180581 |
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