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4. Exclusion and Interchange processes

    1. Comparison of interchange to SRW and Exclusion


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      Problem 4.1.

      [Roberto Oliveira] Consider the interchange process with n particles on n vertices. Can you say the following?

      \begin{align*} t_{\mbox{mix}}^{IP}\lesssim & t_{\mbox{mix}}^{SRW} \log n\,, \\ t_{\mbox{mix}}^{IP} \lesssim & t_{\mbox{mix}}^{SRW,n}\,, \\ t_{\mbox{mix}}^{IP} \asymp & t_{\mbox{mix}}^{SSEP,n/2}\,. \end{align*}
          The first is known for t_{\mbox{rel}} [Caputo et. al]

        • Interchange process on the hypercube


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          Problem 4.2.

          Obtain good bounds on t_{\mbox{mix}}^{IP} on the hypercube \{0,1\}^n.

            • Hitting time comparison


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              Problem 4.3.

              Can you compare the hitting times of the interchange process to hitting times for the SRW on a graph G.

                  Cite this as: AimPL: Markov chain mixing times, available at http://aimpl.org/markovmixing.