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Moment-generating function

Cumulant-generating function

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The cumulant expansion writes
$$
\log\mathbb E[e^{tX}]
=\sum_{n\geq1}\frac{t^n}{n!}\kappa_n(X),
$$
where $\kappa_n$ is the $n$th cumulant. Applied to a fluctuating interaction, it expands the logarithm of the averaged Boltzmann weight in connected expectation values.


Cumulant expansion

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Cumulant expansion

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Cumulant expansion

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