The interchange process on dumbbell graphs has a sharp cutoff exactly when the smaller clique size tends to infinity, with the mixing time scaling crossing at m ~ sqrt(n).
Comparing with octopi
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
Operator inequalities with a geometric flavour have been successful in studying mixing of random walks and quantum mechanics. We suggest a new way to extract such inequalities using the octopus inequality of Caputo, Liggett and Richthammer.
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Mixing time and cutoff phenomenon for the interchange process on dumbbell graphs and the labelled exclusion process on the complete graph
The interchange process on dumbbell graphs has a sharp cutoff exactly when the smaller clique size tends to infinity, with the mixing time scaling crossing at m ~ sqrt(n).