Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2401.12935 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- 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.