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PreprintarXiv licencearXiv

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 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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Cite

BibTeXRIS
BibTeX
@misc{carvalho2026phase,
  title = {{Phase transitions for percolation of words in one dimension}},
  author = {Gustavo O. de Carvalho and Pablo A. Gomes},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05112},
  eprint = {2609.05112},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05112},
}
RIS
TY  - UNPB
TI  - Phase transitions for percolation of words in one dimension
AU  - Gustavo O. de Carvalho
AU  - Pablo A. Gomes
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05112
UR  - https://arxiv.org/abs/2609.05112
AB  - In this paper, we investigate models of percolation of words on 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.
ER  -