-Let us finally present the pseudorandom number generator $\chi_{\textit{15Rairo}}$
+Let us finally present the pseudorandom number generator $\chi_{\textit{15Rairo}}$,
which is based on random walks in $\Gamma_{\{b\}}(f)$.
More precisely, let be given a Boolean map $f:\Bool^{\mathsf{N}} \rightarrow
\Bool^\mathsf{N}$,
a PRNG \textit{Random},
-an integer $b$ that corresponds an iteration number (\textit{i.e.}, the length of the walk), and
+an integer $b$ that corresponds to an iteration number (\textit{i.e.}, the length of the walk), and
an initial configuration $x^0$.
Starting from $x^0$, the algorithm repeats $b$ times
-a random choice of which edge to follow and traverses this edge
-provided it is allowed to traverse it, \textit{i.e.},
+a random choice of which edge to follow, and traverses this edge
+provided it is allowed to do so, \textit{i.e.},
when $\textit{Random}(1)$ is not null.
The final configuration is thus outputted.
This PRNG is formalized in Algorithm~\ref{CI Algorithm}.
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}).
