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diff --git a/vorlesungen/slides/8/markov/markov.tex b/vorlesungen/slides/8/markov/markov.tex
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-%
-% markov.tex
-%
-% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-%
-\bgroup
-\setlength{\abovedisplayskip}{5pt}
-\setlength{\belowdisplayskip}{5pt}
-\begin{frame}[t]
-\frametitle{Markovketten}
-\vspace{-20pt}
-\begin{columns}[t,onlytextwidth]
-\begin{column}{0.48\textwidth}
-\begin{center}
-\begin{tikzpicture}[>=latex,thick]
-
-\def\r{2.2}
-
-\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)});
-\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)});
-\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)});
-\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)});
-\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)});
-
-\draw[->,shorten >= 0.1cm,shorten <= 0.1cm,line width=4pt,color=black!40]
-	(A) -- (C);
-\draw[color=white,line width=8pt] (B) -- (D);
-\draw[->,shorten >= 0.1cm,shorten <= 0.1cm,line width=4pt,color=black!80]
-	(B) -- (D);
-
-\draw[->,shorten >= 0.1cm,shorten <= 0.1cm,line width=4pt,color=black!60]
-	(A) -- (B);
-\draw[->,shorten >= 0.1cm,shorten <= 0.1cm,line width=4pt,color=black!20]
-	(B) -- (C);
-\draw[->,shorten >= 0.1cm,shorten <= 0.1cm,line width=4pt,color=black]
-	(C) -- (D);
-\draw[->,shorten >= 0.1cm,shorten <= 0.1cm,line width=4pt,color=black]
-	(D) -- (E);
-\draw[->,shorten >= 0.1cm,shorten <= 0.1cm,line width=4pt,color=black]
-	(E) -- (A);
-
-\fill[color=white] (A) circle[radius=0.2];
-\fill[color=white] (B) circle[radius=0.2];
-\fill[color=white] (C) circle[radius=0.2];
-\fill[color=white] (D) circle[radius=0.2];
-\fill[color=white] (E) circle[radius=0.2];
-
-\draw (A) circle[radius=0.2];
-\draw (B) circle[radius=0.2];
-\draw (C) circle[radius=0.2];
-\draw (D) circle[radius=0.2];
-\draw (E) circle[radius=0.2];
-
-\node at (A) {$1$};
-\node at (B) {$2$};
-\node at (C) {$3$};
-\node at (D) {$4$};
-\node at (E) {$5$};
-
-\node at ($0.5*(A)+0.5*(B)-(0.1,0.1)$) [above right] {$\scriptstyle 0.6$};
-\node at ($0.5*(B)+0.5*(C)+(0.05,-0.07)$) [above left] {$\scriptstyle 0.2$};
-\node at ($0.5*(C)+0.5*(D)+(0.05,0)$) [left] {$\scriptstyle 1$};
-\node at ($0.5*(D)+0.5*(E)$) [below] {$\scriptstyle 1$};
-\node at ($0.5*(E)+0.5*(A)+(-0.1,0.1)$) [below right] {$\scriptstyle 1$};
-\node at ($0.6*(A)+0.4*(C)$) [above] {$\scriptstyle 0.4$};
-\node at ($0.4*(B)+0.6*(D)$) [left] {$\scriptstyle 0.8$};
-
-\end{tikzpicture}
-\end{center}
-\vspace{-10pt}
-\uncover<7->{%
-\begin{block}{Verteilung}
-\begin{itemize}
-\item<8->
-Welche stationäre Verteilung auf den Knoten stellt sich ein?
-\item<9->
-$P(i)=?$
-\end{itemize}
-\end{block}}
-\end{column}
-\begin{column}{0.48\textwidth}
-\uncover<2->{%
-\begin{block}{\strut\mbox{Übergang\only<3->{s-/Wahrscheinlichkeit}smatrix}}
-$P_{ij} = P(i | j)$, Wahrscheinlichkeit, in den Zustand $i$ überzugehen,
-\begin{align*}
-P
-&=
-\begin{pmatrix}
-   &   & & &1\phantom{.0}\\
-0.6&   & & & \\
-0.4&0.2& & & \\
-   &0.8&1\phantom{.0}& & \\
-   &   & &1\phantom{.0}& 
-\end{pmatrix}
-\end{align*}
-\end{block}}
-\vspace{-10pt}
-\uncover<4->{%
-\begin{block}{Eigenschaften}
-\begin{itemize}
-\item<5-> $P_{ij}\ge 0\;\forall i,j$
-\item<6-> Spaltensumme:
-\(
-\displaystyle
-\sum_{i=1}^n P_{ij} = 1\;\forall j
-\)
-\end{itemize}
-\end{block}}
-\end{column}
-\end{columns}
-\end{frame}