debut d'experimentations

[rairo15.git] / stopping.tex

diff --git a/stopping.tex b/stopping.tex
index e4136889a4471c8ddaa8fe68bb5245fa4878a646..eec08aa44af7534e81b33bb79f7799753763e129 100644 (file)
--- a/stopping.tex
+++ b/stopping.tex
@@ -289,10 +289,10 @@ More formally,
 since $\ov{h}$ is square-free,
 $\ov{h}(X)=\ov{h}(\ov{h}(\ov{h}^{-1}(X)))\neq \ov{h}^{-1}(X)$. It follows
 that $(X,\ov{h}^{-1}(X))\in E_h$. We thus have
 since $\ov{h}$ is square-free,
 $\ov{h}(X)=\ov{h}(\ov{h}(\ov{h}^{-1}(X)))\neq \ov{h}^{-1}(X)$. It follows
 that $(X,\ov{h}^{-1}(X))\in E_h$. We thus have

-$P(X_1=\ov{h}^{-1}(X))=\frac{1}{2{\MATHSF{N}}}$. Now, by Lemma~\ref{lm:h},
+$P(X_1=\ov{h}^{-1}(X))=\frac{1}{2{\mathsf{N}}}$. Now, by Lemma~\ref{lm:h},

 $h(\ov{h}^{-1}(X))\neq h(X)$. Therefore $\P(S_{x,\ell}=2\mid
 $h(\ov{h}^{-1}(X))\neq h(X)$. Therefore $\P(S_{x,\ell}=2\mid

-X_1=\ov{h}^{-1}(X))=\frac{1}{2{\MATHSF{N}}}$, proving that $\P(S_{x,\ell}\leq 2)\geq
-\frac{1}{4{\MATHSF{N}}^2}$.
+X_1=\ov{h}^{-1}(X))=\frac{1}{2{\mathsf{N}}}$, proving that $\P(S_{x,\ell}\leq 2)\geq
+\frac{1}{4{\mathsf{N}}^2}$.

 \end{itemize}
 
 
 \end{itemize}