Sampling Random Cycle-Rooted Spanning Forests on Infinite Graphs - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Sampling Random Cycle-Rooted Spanning Forests on Infinite Graphs

Résumé

On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as limits of probability measures on cycle-rooted spanning forests of increasing sequences of finite graphs. Those probability measures extend the family of already known random spanning forests and can be sampled by a random walks algorithm which generalizes Wilson's algorithm. We show that, unlike for uniform spanning forests, almost surely, all connected components are finite and two-points correlations decrease exponentially fast with the distance.
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Dates et versions

hal-04182926 , version 1 (18-08-2023)

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  • HAL Id : hal-04182926 , version 1

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H Constantin. Sampling Random Cycle-Rooted Spanning Forests on Infinite Graphs. 2023. ⟨hal-04182926⟩
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