Holder continuity of interfaces for scale-invariant Poisson stick soup

Augusto Teixeira; Daniel Ungaretti

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arXiv · 2601.19546

Holder continuity of interfaces for scale-invariant Poisson stick soup

Augusto Teixeira·Daniel Ungaretti

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Abstract

We study the interface of covered and vacant sets in the subcritical phase of a scale-invariant Poisson stick soup on the plane. This model is a natural candidate for scaling limit of some planar models and has connections with long-range percolation on the plane with critical parameter $s=4$. We analyze a family of exploration paths on boxes and prove tightness for this family and Holder continuity for its limiting measures.

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Augusto Teixeira, Daniel Ungaretti. 2026-01-27. Holder continuity of interfaces for scale-invariant Poisson stick soup. https://arxiv.org/abs/2601.19546

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