arXiv Open Access 2024

The local limit of rooted directed animals on the square lattice

Olivier Hénard Édouard Maurel-Segala Arvind Singh

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Abstrak

We consider the local limit of finite uniformly distributed directed animals on the square lattice viewed from the root. Two constructions of the resulting uniform infinite directed animal are given: one as a heap of dominoes, constructed by letting gravity act on a right-continuous random walk and one as a Markov process, obtained by slicing the animal horizontally. We look at geometric properties of this local limit and prove, in particular, that it consists of a single vertex at infinitely many (random) levels. Several martingales are found in connection with the confinement of the infinite directed animal on the non-negative coordinates.

Topik & Kata Kunci

math.PR math.CO

Penulis (3)

Olivier Hénard

Édouard Maurel-Segala

Arvind Singh

Format Sitasi

APA MLA BibTeX

Hénard, O., Maurel-Segala, É., Singh, A. (2024). The local limit of rooted directed animals on the square lattice. https://arxiv.org/abs/2401.12935

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓