Notes on "Adaptive single replica multiple state transition interface sampling" (Du and Bolhuis, 2013)
Probability of an unbiased trajectory $\x^L$: $$ \pi [ \x^L ] = \rho(\x_0) \prod_{i=0}^{L-1} \rho (\x_i \to \x_{i+1}) $$
Normalize using a "partition-function"-like factor: $$ Z \equiv \int \mathcal{D} \x^L \pi [ \x^ L ]$$ (integrated over all possible paths of all lengths)
to yield normalized path probability $$ \mathcal{P}[\x^L] = \frac{\pi [\x^L]}{Z}$$
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