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arXiv · 2609.05112

Phase transitions for percolation of words in one dimension

Gustavo O. de Carvalho·Pablo A. Gomes
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Abstract

In this paper, we investigate models of percolation of words on $\mathbb{Z}_+$ with long-range connections. The underlying graph is oriented and constructed according to a sequence of non-negative ranges. In the first model, the sequence of ranges is considered random and, in the second model, deterministic and non-decreasing. In both cases, we establish a phase transition for the occurrence of percolation of all words simultaneously from the origin.

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Gustavo O. de Carvalho, Pablo A. Gomes. 2026-09-04. Phase transitions for percolation of words in one dimension. https://arxiv.org/abs/2609.05112

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