Notice that the chaos property of $G_f$ given in Sect.\ref{sec:proofOfChaos}
only requires that the graph $\Gamma_{\{b\}}(f)$ is strongly connected.
-Since the $\chi_{\textit{15Rairo}}$ algorithme
-only adds propbability constraints on existing edges,
+Since the $\chi_{\textit{15Rairo}}$ algorithm
+only adds probability constraints on existing edges,
it preserves this property.
which is labeled with $b$ (respectively by $E[\tau]$)
gives the practical mixing time
where the deviation to the standard distribution is less than $10^{-6}$
-(resp. the theoretical upper bound ofstopping time as described in
+(resp. the theoretical upper bound of stopping time as described in
Sect.~\ref{sec:hypercube}).
