Given a random walk on a finite group $(G,S,P)$. Separation distance $s_k$ is defined by the formula $$s_k=|G|\times\max_{ g \in G}\left(\frac{1}{|G|}-Q^k(g)\right).$$
We call an element $\hat{g}_k$ "$k$-minimal" if the probability distribution $Q^k$ on a group $G$ has a minimum value at $\hat{g}_k$. We define a minimal sequence to be a sequence $(\hat{g}_1, \hat{g}_2,...)$ to be any sequence of $k$-minimal elements for each $k>0$.
I don't understand why :
If we have a minimal sequence $(\hat{g}_1, \hat{g}_2,...)$. By definition of the separation distance we have $$s_k=1-|G|*Q^k(\hat{g_k})$$
