# Documentation:Monte Carlo Equilibration

From ALPS

# 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 .

, :

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \left( \begin{array}{cc} N & \sum_i x_i \\ \sum_i x_i & \sum_i x_i^2 \end{array} \right) \left(\beta_0 \\ \beta_1\right) = \left(\sum_i y_i \\ \sum_i x_i y_i \right) **