 ### fix math

parent 60704d66
Pipeline #58155 passed with stages
in 1 minute and 33 seconds
 ... ... @@ -79,12 +79,12 @@ case we could instead try to sample from a nearby distribution $p_\text{sample}( In this way we can make sure to approximately focus on the physically relevant configurations. Doing this requires us to rewrite the integral as $$\begin{split}$$\begin{eqnarray} \int p_\text{real}(R) A(R) dR = & \int p_\text{sampling}(R) \underbrace{\frac{p_\text{real}(R)}{p_\text{sampling}(R)}}}_{=w(R)} A(R) dR\\ \int p_\text{sampling}(R) \underbrace{\frac{p_\text{real}(R)}{p_\text{sampling}(R)}}_{=w(R)} A(R) dR\\ = & \int p_\text{sampling}(R) w(R) A(R) dR\\ \approx & \frac{1}{N} \sum_{i=1}^N w(R_i) A(R_i) \tag{3} \end{split}$$\end{eqnarray}$$ where the configurations$R_i$are now sampled from$p_\text{sampling}(R)$. When using this approximate probability distribution we thus have to introduce *weights*$w(R)\$ into the average. ... ...
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