The spectrum and convergence rates of exclusion and interchange processes on the complete graph
Journal article, 2017

We give a short and completely elementary method to find the full spectrum of the exclusion process and a nicely limited superset of the spectrum of the interchange process (a.k.a.\ random transpositions) on the complete graph. In the case of the exclusion process, this gives a simple closed form expression for all the eigenvalues and their multiplicities. This result is then used to give an exact expression for the distance in \( L^2 \) from stationarity at any time and upper and lower bounds on the convergence rate for the exclusion process. In the case of the interchange process, upper and lower bounds are similarly found. Our results strengthen or reprove many known results about the mixing time for the two processes in a very simple way.


Malin Palö Forsström

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Johan Jonasson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Theoretical Probability

0894-9840 (ISSN) 1572-9230 (eISSN)

Vol. 30 2 639-654


Basic sciences

Subject Categories

Probability Theory and Statistics



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