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In this paper we consider Bernoulli percolation on an infinite connected bounded degrees graph $G$. Assuming the uniqueness of the infinite open cluster and a quasi-multiplicativity of crossing probabilities, we prove the existence of Kesten’s incipient infinite cluster. We show that our assumptions are satisfied if $G$ is a slab $\mathbb{Z} ^2\times \{0,\ldots ,k\}^{d-2}$ ($d\geq 2$, $k\geq 0$). We also argue that the quasi-multiplicativity assumption should hold for $G=\mathbb{Z} ^d$ when $d<6$, but not when $d>6$.

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Basu, Deepan -  Sapozhnikov, Artem - 

Id.: 69834642

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveincipient infinite cluster - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2017 The Institute of Mathematical Statistics and the Bernoulli Society

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 1083-589X

Fecha de contribución: 27-may-2017


* Electron. Commun. Probab.
* doi:10.1214/17-ECP56

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