Changeset - b43c29412d5d
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Tom Bannink - 8 years ago 2017-05-29 08:51:35
tombannink@gmail.com
Add note on probability independence claim
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@@ -414,6 +414,12 @@ The proof of claim \ref{claim:expectationsum} also proves the following claim
 
    \end{align*}
 
up to any order in $p$.
 
\end{claim}
 
Since the left hand side is defined as
 
\begin{align*}
 
    \mathbb{P}[\mathrm{NZ}_{j_1} , \mathrm{NZ}_{j_2} |\;\text{start in }b]
 
    = \sum_{\substack{\xi\in\paths{b}\\j_1,j_2 \text{ not 0 in } \xi}} \mathbb{P}[\xi]
 
\end{align*}
 
we see that all such paths $\xi$ can be split into paths $\xi_1\in\paths{b_1}$ and $\xi_2\in\paths{b_2}$ and by the same reasoning as in the proof of claim \ref{claim:expectationsum}, we obtain the right hand side.
 

	
 
\newpage
 
    \subsection{Sketch of the (false) proof of the linear bound \ref{it:const}}
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