\documentclass[letterpaper,11pt]{amsart}

%\usepackage{graphicx,color,epsfig}
\usepackage{amsfonts,amsmath,amssymb,amsthm}
%\usepackage{comment}
%\usepackage{hyperref}
%\usepackage{mathtools}

%%I USE THESE COMMANDS TO SET THE PAPER DIMENSIONS AND MARGINS FOR THE PAPER

%\setlength{\voffset}{9mm}
%\setlength{\hoffset}{-3mm}
\setlength{\textwidth}{6.5in}
%\setlength{\marginparwidth}{.5in}
\setlength{\marginparsep}{.5in}
\setlength{\oddsidemargin}{.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\evensidemargin}{0in}
\setlength{\paperheight}{11in}
\setlength{\paperwidth}{8.5in}
%%%\setlength{\footskip}{2\baselineskip}
%\linespread{1.5}			
\setlength{\topmargin}{0in}
%\setlength{\headheight}{0pt}
%\setlength{\headsep}{0pt}
%%\setlength{\textheight}{8.85in}
\setlength{\textheight}{8.75in}

\raggedbottom
%\flushbottom


%%%%%%%%THEOREM ENVIRONMENTS....

\newtheorem{thm}{Theorem}[section]
\newtheorem{prop}[thm]{Proposition}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{conj}[thm]{Conjecture}
\newtheorem{asm}{Assumption}
\newtheorem{op}[thm]{Question}


\theoremstyle{remark}
\newtheorem{rem}[thm]{Remark}

\theoremstyle{definition}
\newtheorem{defn}{Definition}
\newtheorem{ex}[thm]{Example}


%%%%%%% MATH LATEX SHORTCUTS

%blackboard bold letters
\newcommand{\C}{\mathbb C}    % For Complex numbers
\newcommand{\N}{\mathbb N}     % For Natural numbers
\newcommand{\Q}{\mathbb Q}     % For Rational numbers
\newcommand{\R}{\mathbb R}     % For Real numbers
\newcommand{\Z}{\mathbb Z}     % For Integers

%greek letters
\renewcommand{\a}{\alpha}
\renewcommand{\b}{\beta}
\renewcommand{\c}{\gamma}
\renewcommand{\d}{\delta}
%\renewcommand{\e}{\epsilon}
\newcommand{\e}{\varepsilon}
\newcommand{\del}{\partial}
\newcommand{\w}{\omega}
\renewcommand{\O}{\Omega}
\renewcommand{\l}{\lambda}
\renewcommand{\L}{\Lambda}
\newcommand{\s}{\sigma}
\renewcommand{\th}{\theta}

\newcommand{\ra}{\rightarrow}
\newcommand{\Ra}{\Rightarrow}
\newcommand{\bigo}{\mathcal{O}}

%opening
\title[SHORT TITLE]{FULL TITLE}


\author{AUTHOR 1}
\address{AUTHOR 1 NAME \\ ADDRESS \\ CITY}
%\email{}
%\urladdr{}
%\thanks{}

\author{AUTHOR 2}
\address{AUTHOR 2 NAME \\ ADDRESS \\ CITY}
%\email{}
%\urladdr{}
%\thanks{}


%\date{11/10/09}

%\subjclass[2010]{ }
%\keywords{ }


\begin{document}

%\begin{abstract}
% ABSTRACT GOES HERE...
%\end{abstract}

\maketitle

\section{Introduction}

The introduction should start here.

Our main result will be.
\begin{thm}\label{CLT}
If $X_1,X_2,\ldots$ are independent, identically distributed random variables with $E[X_1]=0$ and $\s^2 = E[X_1^2] < \infty$, then 
\[
 \lim_{n\rightarrow\infty} P\left( \frac{\sum_{k=1}^n X_k }{\s \sqrt{n}} \leq x \right) = \int_{-\infty}^x \frac{1}{\sqrt{2\pi}} e^{-z^2/2} \, dz, \qquad \forall x \in \R. 
\]
\end{thm}
\begin{proof}
 We will use characteristic functions $\phi(t) = E[e^{itX_1}]$....
\end{proof}

A really cool paper is \cite{kRDE} by Kesten. Everyone should read this paper. 

To reference Theorem \ref{CLT} we use a reference command. 
The following is a labeled equation. 
\begin{equation}\label{euler}
 e^{i\pi} + 1 = 0. 
\end{equation}
Equation \eqref{euler} was proved by Euler.

To produce multi-lined math displays use the ``align'' environment. 
\begin{align*}
 \sum_{k=0}^\infty P(X > k)
&= \sum_{k=0}^\infty \sum_{n=k+1}^\infty P(X=n) \\
&= \sum_{n=1}^\infty \sum_{k=0}^{n-1} P(X=n) \\
&= \sum_{n=1}^\infty n P(X=n) \\
&= E[X]. 
\end{align*}


There are several ways to produce matrices in \LaTeX, but the easiest is to use the ``pmatrix'' command. 
\[
\begin{pmatrix}
 1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
\]

\begin{thebibliography}{99}

\bibitem{kRDE}
Harry Kesten.
\newblock {Random difference equations and renewal theory for products of
  random matrices}.
\newblock {\em Acta Math.}, 131:207--248, 1973.
\end{thebibliography}

\end{document}
