# Documentation:Monte Carlo Equilibration

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Revision as of 12:34, 9 September 2013 by Tamama (talk | contribs) (→Error in slope of best-fitted line)

## Contents

# Monte Carlo equilibration

## Theory

We have a timeseries of N measurements obtained from a Monte Carlo simulation, i.e. .

Suppose (s.t. ) is the least-squares best fitted line, we attempt to minimize w.r.t. and .

, :

### Slope of best-fitted line

### Error in slope of best-fitted line

Denoting , we have:

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \Rightarrow \mathrm{Var}({\beta_1}) = \sigma_{\beta^_1}2 = \frac{\sigma_y^2}{\sum_i (x_i - \bar{x}_i)^2} **