Files
@ 2d71071d9d58
Branch filter:
Location: AENC/resampling_chain/diagram_circle_lemma.tex - annotation
2d71071d9d58
2.2 KiB
text/x-tex
Add small update to splitting lemma proof
aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 | \documentclass{standalone}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{parskip}
\usepackage[usenames,dvipsnames]{color}
\usepackage[hidelinks]{hyperref}
\renewcommand*{\familydefault}{\sfdefault}
\usepackage{bbm} %For \mathbbm{1}
%\usepackage{bbold}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\def\r{4};
\def\step{15};
% Line and circles
\foreach \a in {0,...,23} {
\draw[-] ({\a*\step}:\r) -- ({(\a+1)*\step}:\r);
\draw ({\a*\step}:\r) circle (0.05);
}
% Red dots
\foreach \a in {2,3,6,8,9,10,11,14,15,17,20} {
\draw[fill,red] ({\a*\step}:\r) circle (0.09);
}
% Blue squares
\foreach \a in {2,3,20} {
\draw[fill,blue] ({\a*\step}:{\r-0.3})+(-0.1,-0.1) rectangle +(0.1,0.1);
}
% Green triangles
\foreach \a in {6,8,9,10,11,14,15,17} {
\draw[fill,green] ({\a*\step}:{\r-0.3}) +(-0.15,-0.1) -- +(0.15,-0.1) -- +(0,0.15);
}
% Legend
\draw (-1,0)+(-0.5,-1) rectangle +(2.6,1);
\draw[fill,red] (-1.1,0.5) circle (0.09);
\draw[fill,blue] (-1.1,0) +(-0.1,-0.1) rectangle +(0.1,0.1);
\draw[fill,green] (-1.1,-0.5) +(-0.15,-0.1) -- +(0.15,-0.1) -- +(0,0.15);
\draw[anchor=west] (-1,0.5) node {$I$};
\draw[anchor=west] (-1,0) node {$I\cap [{\color{gray}n}{-l},r]_0$};
\draw[anchor=west] (-1,-0.5) node {$I\setminus[{\color{gray}n}{-l},r]_0$};
% Bigger circle
\foreach \a in {-5,...,3} {
\draw[-,dashed] ({\a*\step}:\r+1) -- ({(\a+1)*\step}:\r+1);
%\draw ({\a*\step}:\r+1) circle (0.05);
}
\draw ({-5*\step}:\r+1) +(0.2,-0.2) node {${\color{gray}n}{-l}$};
\draw ({4*\step}:\r+1) +(0.2,0.2) node {$r$};
%
% Arrows with labels
%
% 0
\draw ({0*\step}:\r-0.3) node {$0$};
% 1
\draw ({1*\step}:\r-0.3) node {$1$};
% n/2
\draw ({12*\step}:\r-0.3) node {$\frac{n}{2}$};
% n-1
\draw ({-1*\step}:\r-0.3) +(-0.4,0) node {${\color{gray}n}{-1}$};
% i_*
\draw[->] ({10*\step}:\r-1) -- ({10*\step}:\r-0.2);
\draw ({10*\step}:\r-1) +(0.3,0) node {$i_*$};
% j
\draw[->] ({0*\step}:\r-1.3) -- ({0*\step}:\r-0.8);
\draw ({0*\step}:\r-1) +(-0.4,0) node {$j$};
\end{tikzpicture}
\end{document}
|