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The Constrained-degree percolation model

Author

Listed:
  • de Lima, B.N.B.
  • Sanchis, R.
  • dos Santos, D.C.
  • Sidoravicius, V.
  • Teodoro, R.

Abstract

In the Constrained-degree percolation model on a graph (V,E) there are a sequence, (Ue)e∈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 Ue, 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 L2, 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.

Suggested Citation

  • de Lima, B.N.B. & Sanchis, R. & dos Santos, D.C. & Sidoravicius, V. & Teodoro, R., 2020. "The Constrained-degree percolation model," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5492-5509.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5492-5509
    DOI: 10.1016/j.spa.2020.03.014
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    Cited by:

    1. Hartarsky, Ivailo & N.B. de Lima, Bernardo, 2022. "Weakly constrained-degree percolation on the hypercubic lattice," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 128-144.

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