Print Email Facebook Twitter Scale-free percolation mixing time Title Scale-free percolation mixing time Author Cipriani, A. (TU Delft Applied Probability) Salvi, Michele (University of Rome Tor Vergata) Date 2024 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 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. Subject Degree distributionMixing timeRandom graphScale-free percolation To reference this document use: http://resolver.tudelft.nl/uuid:1f60409e-4439-45be-ace1-1a9bc05a1812 DOI https://doi.org/10.1016/j.spa.2023.104236 Embargo date 2024-04-29 ISSN 0304-4149 Source Stochastic Processes and their Applications, 167 Bibliographical note 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. Part of collection Institutional Repository Document type journal article Rights © 2024 A. Cipriani, Michele Salvi Files PDF 1_s2.0_S0304414923002089_main.pdf 2.07 MB Close viewer /islandora/object/uuid:1f60409e-4439-45be-ace1-1a9bc05a1812/datastream/OBJ/view