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Equivalence Between Nested Gibbs Measures and Log-Linear Combinations of Gibbs Measures

arXiv · AI, language, vision and robotics · article · Sep 17, 2026 · UTC

In this paper, three operations on Gibbs probability measures are studied. The first operation, often referred to as renormalization, takes one Gibbs probability measure and generates a new Gibbs measure by normalizing a power of its density. This normalization has a twofold effect: it changes the regularization factor and concentrates the support within a subset of the original support. Interestingly, these effects can be independently controlled by different parameters. The second operation consists of a normalized log-linear combination of the densities of Gibbs probability measures. The th

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