From 988f9c51eeae9751e11cdaf34302ee96677a10da Mon Sep 17 00:00:00 2001 From: couchot Date: Sat, 14 Mar 2015 09:59:57 +0100 Subject: [PATCH 1/1] typos --- stopping.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/stopping.tex b/stopping.tex index faab606..25e458d 100644 --- a/stopping.tex +++ b/stopping.tex @@ -284,7 +284,7 @@ Indeed, $\P(S_{X,\ell}=1)=\frac{1}{{\mathsf{N}}}\geq \frac{1}{{\mathsf{N}}^2}$. \item otherwise, $h(X)=\ell$, then $\P(S_{X,\ell}=1)=0$. -But in this case, intutively, it is possible to move +But in this case, intuitively, it is possible to move from $X$ to $\ov{h}^{-1}(X)$ (with probability $\frac{1}{N}$). And in $\ov{h}^{-1}(X)$ the $l$-th bit can be switched. More formally, @@ -331,7 +331,7 @@ One has $\ts^\prime=\sum_{i=1}^{{\mathsf{N}}}W_i$. At position $X$ with $i-1$ fair bits, we do not obtain a new fair if $Z$ is one of the $i-1$ already fair bits or if $Z$ is a new fair bit but $h(X)$ is $Z$. -This occures with probability +This occurs with probability $p = \frac{i-1}{{\mathsf{N}}} + \frac{n-i+1}{\mathsf{N}}.\frac{1}{\mathsf{N}} =\frac{i(\mathsf{N}-1) +1}{\mathsf{N^2}} @@ -375,7 +375,7 @@ lemma~\ref{prop:lambda} and~\ref{lm:stopprime}. Notice that the calculus of the stationary time upper bound is obtained under the following constraint: for each vertex in the $\mathsf{N}$-cube there are one ongoing arc and one outgoing arc that are removed. -The calculus does not consider (balanced) hamiltonian cycles, which +The calculus does not consider (balanced) Hamiltonian cycles, which are more regular and more binding than this constraint. In this later context, we claim that the upper bound for the stopping time should be reduced. -- 2.39.5