4. Exclusion and Interchange processes

Comparison of interchange to SRW and Exclusion
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*} 
Interchange process on the hypercube
Problem 4.2.
Obtain good bounds on $t_{\mbox{mix}}^{IP}$ on the hypercube $\{0,1\}^n$. 
Hitting time comparison
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.