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A direct comparison between the mixing time of the interchange process with "few" particles and independent random walks
Jonathan Hermon, Richard Pymar
We consider the interchange process with particles () on -vertex hypergraphs in which each hyperedge rings at rate . When rings, the particles occu…
Universality of cutoff for graphs with an added random matching
Jonathan Hermon, Allan Sly, Perla Sousi
We establish universality of cutoff for simple random walk on a class of random graphs defined as follows. Given a finite graph with even we define a random graph $…
Further Results and Discussions on Random Cayley Graphs
Jonathan Hermon, Sam Olesker-Taylor
Consider the random Cayley graph of a finite group with respect to generators chosen uniformly at random, with . The results of this article supp…
Cutoff for Random Walks on Upper Triangular Matrices
Jonathan Hermon, Sam Olesker-Taylor
Consider the random Cayley graph of a finite group with respect to generators chosen uniformly at random, with (ie ). A co…
The interchange process on high-dimensional products
Jonathan Hermon, Justin Salez
We resolve a long-standing conjecture of Wilson (2004), reiterated by Oliveira (2016), asserting that the mixing-time of the unit-rate Interchange Process on the -dimensional hy…
Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution
Jonathan Hermon, Tom Hutchcroft
Let be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on . We prove that if is nonamenable and then there exists a p…