# Errors evaluation for a Markov chain_Questions

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You can insert math formulæ using LaTeX code: e.g. typing
[[math]]
\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}
[[math]]
yields:
$\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}$

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## Questions and Remarks:

• Q: I have a problem with the formula (1), namely the formula which gives the statistical error in our Markov chain data from the autocorrelation function. I would expect that we recover the usual formula ( sqrt(var/N) ) if the data are uncorellated (ie if C(n) = 0 for n > 0), but here I get sqrt(2var/N).

• A: Yes you are right, there is a small mistake in Eq.(1). The correct formula is
$\langle\xi\rangle= \frac{1}{N}\sum_{n=0}^N \xi_n \pm \frac{\sqrt{ C(0) +2 \sum_{n=1}^N C(n)}}{\sqrt{N}}\qquad\qquad (1)$