| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

4. Exclusion and Interchange processes

    1. Comparison of interchange to SRW and Exclusion


      Add remark

      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


          Add remark

          Problem 4.2.

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

            • Hitting time comparison


              Add remark

              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.