deletions | additions       diff --git a/time_series_convergence.tex b/time_series_convergence.tex  index 0012939..bd7d072 100644  --- a/time_series_convergence.tex  +++ b/time_series_convergence.tex 
...
\centering  \includegraphics[width=\linewidth]{./figures/time_series.png}  \caption{Time series for a $n=32$ particle system at packing fraction $\phi_{HS}=0.7$ and $\phi_{SS}=0.88$ ran for about $2 \times 10^6$ MCMC steps, one $1/100$ of all points are shown.}  \label{fig:timeseries}  \end{minipage}  \label{fig:timeseries}  \end{figure}  Since we do not know how long it will take to reach the boundary of the basin and we cannot afford to run the calculations for an exceedingly large number of steps, we would like to develop an automated way of adapting the calculation length to reach some target relative statistical error. The statistical error $\Delta_A$, the root-mean square deviation of the sample mean $\overline{A}$ from the true expectation value $\langle A \rangle$, is given by: