ajout de la partie chaos

[rairo15.git] / stopping.tex

diff --git a/stopping.tex b/stopping.tex
index 567ab014f8a246bff2cd12447453c7c598c0898f..19f1feb2981dd1752efedd535855148b237f3d8b 100644 (file)
--- a/stopping.tex
+++ b/stopping.tex
@@ -176,14 +176,16 @@ let $S_{X,\ell}$ be the
 random variable that counts the number of steps 
 from $X$ until we reach a configuration where
 $\ell$ is fair. More formally
 random variable that counts the number of steps 
 from $X$ until we reach a configuration where
 $\ell$ is fair. More formally

-$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,\.)\text{ and } X_0=X\}.$$
+$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,.)\text{ and } X_0=X\}.$$

 
  We denote by
 $$\lambda_h=\max_{X,\ell} S_{X,\ell}.$$
 
 
 \begin{Lemma}\label{prop:lambda}
 
  We denote by
 $$\lambda_h=\max_{X,\ell} S_{X,\ell}.$$
 
 
 \begin{Lemma}\label{prop:lambda}

-If $\ov{h}$ is a square-free bijective function, then one has $E[\lambda_h]\leq 8n^2.$
+If $\ov{h}$ is a square-free bijective function, then the inequality 
+$E[\lambda_h]\leq 8n^2$ is established.
+

 \end{Lemma}
 
 \begin{proof}
 \end{Lemma}
 
 \begin{proof}