Double \rightsquigarrow?

Question

I came across this symbol in a probability book but don’t know how to type it.

Answer 1

UPDATE: This is not a complete solution. As pointed out in the comments by Ruixi Zhang, substack by default puts its contents in \scriptstyle. So unless you manually specify the correct math level size you want (\displaystyle, \textstyle etc) the size of the arrows isn't truly correct and won't scale automatically.

Original answer

Here is a proposal using substack.

You can adjust the vertical separation between the arrows by adjusting [-2em] after \\. I've also wrapped the substack in mathrel. This modifies the spacing around the substack to that of a relation, such as =.

\documentclass{article}
\usepackage{amsmath,amssymb}

\newcommand{\doublerightsquigarrow}{\mathrel{\substack{\displaystyle\rightsquigarrow\\[-2em]\displaystyle\rightsquigarrow}}}

\begin{document}
\[
(\mathbb{F}_n - F)  \doublerightsquigarrow  \mathcal{H} \circ F
\]
\end{document}

Answer 2

Here is an alternative to @Milo’s solution, which takes care of getting the correct size in each of \displaystyle, \textstyle, \scriptstyle and \scriptscriptstyle. No additional packages needed.

The solution is essentially stacking arrows. However, none of the solutions suggested in that linked post addressed the sizing problem. Note that if you were to use @Milo’s solution in \displaystyle or \textstyle, you should probably add \textstyle in \substack as in @SBoonto’s solution.

To properly design the separation between the two arrows, I took inspiration from this answer by @wipet. But instead of \vbox, we should use \vcenter to construct our symbol. Note that the resulting double arrows are closer and, IMHO, more suitable to be viewed as one symbol.

Also, note that I called the new symbol \doublerightsquigarrows instead of \doublerightsquigarrow. The \stack@two@symbols macro can be used to create other stacked symbols (Of course, you use it within a pair of \makeatletter and \makeatother).

\documentclass{article}
\usepackage{amssymb}% no need for `amsmath'

\linespread{2}\selectfont% for better visual

\makeatletter
\newcommand*{\doublerightsquigarrows}{%
  \mathrel{\mathchoice
    {\stack@two@symbols{text}{display}{\rightsquigarrow}{\rightsquigarrow}}%
    {\stack@two@symbols{text}{text}{\rightsquigarrow}{\rightsquigarrow}}%
    {\stack@two@symbols{script}{script}{\rightsquigarrow}{\rightsquigarrow}}%
    {\stack@two@symbols{scriptscript}{scriptscript}{\rightsquigarrow}{\rightsquigarrow}}%
  }%
}
% just for fun
\newcommand*{\crazyarrows}{%
  \mathrel{\mathchoice
    {\stack@two@symbols{text}{display}{\mapsto}{\Leftarrow}}%
    {\stack@two@symbols{text}{text}{\mapsto}{\Leftarrow}}%
    {\stack@two@symbols{script}{script}{\mapsto}{\Leftarrow}}%
    {\stack@two@symbols{scriptscript}{scriptscript}{\mapsto}{\Leftarrow}}%
  }%
}
% syntax of \stack@two@symbols{#1}{#2}{#3}{#4}:
%    #1: font dimension parameters, `text', `script' or `scriptscript';
%    #2: math styles, `display', `text', `script' or `scriptscript';
%    #3: top symbol;
%    #4: bottom symbol.
\def\stack@two@symbols#1#2#3#4{%
  \vcenter{%
  \baselineskip=\fontdimen17\csname#1font\endcsname2\advance\baselineskip by\fontdimen14\csname#1font\endcsname2%
  \halign{\hfil$\csname#2style\endcsname##$\hfil\cr#3\cr#4\cr}}%
}
\makeatother

\newcommand*{\test}[1]{%
  \makebox[10em][r]{\texttt{\textbackslash#1}}:
  $\csname#1\endcsname \sqrt{\frac{n}{2 \log \log n}} (\mathbb{F}_n - F) \doublerightsquigarrows \mathcal{H} \circ F$%
}
\newcommand*{\testcrazy}[1]{%
  \makebox[10em][r]{\texttt{\textbackslash#1}}:
  $\csname#1\endcsname \sqrt{\frac{n}{2 \log \log n}} (\mathbb{F}_n - F) \crazyarrows \mathcal{H} \circ F$%
}

\begin{document}
Double rightsquig arrows\par
\test{displaystyle}\par
\test{textstyle}\par
\test{scriptstyle}\par
\test{scriptscriptstyle}\par
Crazy arrows\par
\testcrazy{displaystyle}\par
\testcrazy{textstyle}\par
\testcrazy{scriptstyle}\par
\testcrazy{scriptscriptstyle}
\end{document}

Answer 3

The vertical gap between the two arrows is governed by the 12\LMpt (optional argument to \stackanchor).

\documentclass{article}
\usepackage{amssymb,stackengine,scalerel}
\newcommand\doublerightsquigarrow{%
  \mathrel{\ThisStyle{\def\stacktype{L}\ensurestackMath{
    \stackanchor[12\LMpt]{\SavedStyle\rightsquigarrow}{\SavedStyle\rightsquigarrow}
  }}}
}
\begin{document}
\[
                    (\mathbb{F}_n - F)  \doublerightsquigarrow  \mathcal{H} \circ F
\]
\[
\scriptstyle        (\mathbb{F}_n - F)  \doublerightsquigarrow  \mathcal{H} \circ F
\]
\[
\scriptscriptstyle  (\mathbb{F}_n - F)  \doublerightsquigarrow  \mathcal{H} \circ F
\]
\end{document}

Answer 4

We can easily reproduce the picture:

\documentclass{article}
\usepackage{amsmath,amssymb}

\begin{document}

\[
\limsup_{n\to\infty} \sqrt{\frac{n}{2\log\log n}}
(\mathbb{F}_n-F)
\mathrel{\begin{matrix}
\rightsquigarrow \\
\rightsquigarrow
\end{matrix}}
\mathcal{H}\circ F
\]

\end{document}

However, if you prefer less vertical space (and you should), here's how.

\documentclass{article}
\usepackage{amsmath,amssymb}

\makeatletter
% find a better name
\newcommand{\doublerightsquigarrow}{%
  \mathrel{\mathpalette\double@rightsquigarrow\relax}%
}
\newcommand\double@rightsquigarrow[2]{%
  \vcenter{
    \m@th % no math surround
    \baselineskip=\z@ % let \lineskip play
    \lineskiplimit=\z@
    \lineskip=1pt % or whatever
    \hbox{$#1\rightsquigarrow$}
    \hbox{$#1\rightsquigarrow$}
  }%
}
\makeatother

\begin{document}

\[
\limsup_{n\to\infty} \sqrt{\frac{n}{2\log\log n}}\,(\mathbb{F}_n-F)
\doublerightsquigarrow
\mathcal{H}\circ F
\]

$A\doublerightsquigarrow B$

$\scriptstyle A\doublerightsquigarrow B$

$\scriptscriptstyle A\doublerightsquigarrow B$

\end{document}