From: Pierre-Cyrille Héam <pheam@femto-st.fr>
Date: Thu, 30 Jun 2016 09:20:54 +0000 (+0200)
Subject: pch
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/commitdiff_plain/3434a6bb461a09975ace82f172dbf7ea647d882b?ds=sidebyside;hp=-c

pch
---

3434a6bb461a09975ace82f172dbf7ea647d882b
diff --git a/main.pdf b/main.pdf
index 58e266f..ff7928d 100644
Binary files a/main.pdf and b/main.pdf differ
diff --git a/stopping.tex b/stopping.tex
index 284fc49..539d653 100644
--- a/stopping.tex
+++ b/stopping.tex
@@ -60,12 +60,14 @@ $$\tv{\pi-\mu}=\frac{1}{2}\sum_{X\in\Bool^{\mathsf{N}}}|\pi(X)-\mu(X)|.$$ Moreov
 $\nu$ is a distribution on $\Bool^{\mathsf{N}}$, one has
 $$\tv{\pi-\mu}\leq \tv{\pi-\nu}+\tv{\nu-\mu}$$
 
-Let $P$ be the matrix of a Markov chain on $\Bool^{\mathsf{N}}$. $P(X,\cdot)$ is the
-distribution induced by the $X$-th row of $P$. If the Markov chain induced by
-$P$ has a stationary distribution $\pi$, then we define
+Let $P$ be the matrix of a Markov chain on $\Bool^{\mathsf{N}}$. For any
+$X\in \Bool^{\mathsf{N}}$, let $P(X,\cdot)$ be the distribution induced by the
+${\rm bin}(X)$-th row of $P$, where ${\rm bin}(X)$ is the integer whose
+binary encoding is $X$. If the Markov chain induced by $P$ has a stationary
+distribution $\pi$, then we define
 $$d(t)=\max_{X\in\Bool^{\mathsf{N}}}\tv{P^t(X,\cdot)-\pi}.$$
 
-\ANNOT{incohérence de notation $X$ : entier ou dans $B^N$ ?}
+%\ANNOT{incohérence de notation $X$ : entier ou dans $B^N$ ?}
 and
 
 $$t_{\rm mix}(\varepsilon)=\min\{t \mid d(t)\leq \varepsilon\}.$$