
## 4. Exclusion and Interchange processes

1. ### 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*}
The first is known for $t_{\mbox{rel}}$ [Caputo et. al]
• ### 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.