Cover times - spectral

N/A

Cover times, blanket times, and majorizing measures We exhibit a strong connection between cover times of graphs, Gaussian processes, and Talagrand's theory of majorizing measures. In particular, we show that the cover time of any graph $G$ is equivalent, up to universal constants, to the square of the expected maximum of the Gaussian free field on $G$, scaled by the number of edges in $G$. This allows us to resolve a number of open questions. We give a deterministic polynomial-time algorithm that computes the cover time to within an O(1) factor for any graph, answering a question of Aldous a

saved by

• Didier Lampard
• Luke Hawranick

related reading

• refining bounds - cover timesarxiv.org
• Arborescences of Random Covering Graphsarxiv.org
• piercing intervals - gyarfasarxiv.org
• my projectsdan-iel-lee.vercel.app
• [2604.27639] How large part of a graph can be covered by the neighborhoods of k vertices?arxiv.org
• Patrick Morrissites.google.com
• [2604.04115] Gallai 3-colourings of random graphsarxiv.org
• CSE 599 Recent Developments in Approximation Algorithmshomes.cs.washington.edu
• Random Turán Problems for Graphs with a Vertex Complete to One Partarxiv.org
• nullstellensatzweb.math.princeton.edu
• random subgraphs rainbowarxiv.org
• Nicholas Cook - Duke Mathsites.math.duke.edu