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The spectrum and convergence rates of exclusion and interchange processes on the complete graph

Malin Palö Forsström (Institutionen för matematiska vetenskaper, matematisk statistik) ; Johan Jonasson (Institutionen för matematiska vetenskaper, matematik)
Journal of theoretical probability (0894-9840). Vol. 30 (2017), 2, p. 639-654.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2016-12-19. Senast ändrad 2017-07-04.
CPL Pubid: 246353

 

Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)
Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Sannolikhetsteori och statistik

Chalmers infrastruktur