# Documentation:Monte Carlo Equilibration

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## 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:

### Hypothesis testing: Monte Carlo statistics has reached steady state?

Using the standard z-test, we reject at confidence interval $\alpha$ if