From 8845f0ad0e1fda56b399e8c451712a1cd6b3afe4 Mon Sep 17 00:00:00 2001 From: couchot Date: Fri, 20 Feb 2015 10:15:14 +0100 Subject: [PATCH] typo --- stopping.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/stopping.tex b/stopping.tex index 567ab01..19f1feb 100644 --- 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 -$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,\.)\text{ and } X_0=X\}.$$ +$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,.)\text{ and } X_0=X\}.$$ We denote by $$\lambda_h=\max_{X,\ell} S_{X,\ell}.$$ \begin{Lemma}\label{prop:lambda} -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} -- 2.39.5