Deformation Theory of Boltzmann Distributions. (arXiv:2210.13772v2 [hep-lat] UPDATED)

Consider a one-parameter family of Boltzmann distributions $p_t(x) =
\tfrac{1}{Z_t}e^{-S_t(x)}$. We study the problem of sampling from $p_{t_0}$ by
first sampling from $p_{t_1}$ and then applying a transformation
$\Psi_{t_1}^{t_0}$ to the samples so that to they follow $p_{t_0}$. We derive
an equation relating $\Psi$ and the corresponding family of unnormalized
log-likelihoods $S_t$. We demonstrate the utility of this idea on the $\phi^4$
lattice field theory by extending its defining action $S_0$ to a family of
actions $S_t$ and finding a …

arxiv boltzmann theory