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Probabilidade e Combinatória

Título |
The Constrained-degree percolation model |

Expositor |
Bernardo N. B. de Lima
UFMG |

Data |
Quarta-feira, 15 de janeiro de 2020, 15:30 |

Local |
Sala 345 |

Resumo |

In the Constrained-degree percolation model on a graph $(V,E)$ there are a sequence, $(U_e)_{e\in E}$, of i.i.d. random variables with distribution $U[0,1]$ and a positive integer $k$. Each bond $e$ tries to open at time $U_e$, it succeeds if both its end-vertices would have degrees at most $k-1$. We prove a phase transition theorem for this model on the square lattice $\mathbb{L}^2$, as well as on the d-ary regular tree. We also prove that on the square lattice the infinite cluster is unique in the supercritical phase.

Joint work with R. Sanchis, D. dos Santos, V. Sidoravicius and R. Teodoro