Skip to main content

A lower bound for the critical probability of the square lattice site percolation

Summary

We prove by elementary combinatorial considerations that the critical probability of the square lattice site percolation is larger than 0.503478.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Higuchi, Y.: Coexistence of the infinite () clusters: a remark on the square lattice site percolation. Z. Wahrscheinlichkeitstheorie verw. Gebiete 61, 75–81 (1982)

    Google Scholar 

  2. 2.

    Kesten, H.: Percolation for Mathematicians. Boston-Basel-Stuttgart: Birkhäuser 1982

    Google Scholar 

  3. 3.

    Russo, L.: A note on percolation. Z. Wahrscheinlichkeitstheorie verw. Gebiete 43, 39–48 (1978)

    Google Scholar 

  4. 4.

    Russo, L.: On the critical percolation probabilities. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56, 229–238 (1981)

    Google Scholar 

  5. 5.

    Shante, V.K.S., Kirkpatrick, S.: An introduction to percolation theory. Advances in Phys. 20, 325–357 (1971)

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

Work supported by the Central Research Found of the Hungarian Academy of Sciences (Grant No. 476/82)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tóth, B. A lower bound for the critical probability of the square lattice site percolation. Z. Wahrscheinlichkeitstheorie verw Gebiete 69, 19–22 (1985). https://doi.org/10.1007/BF00532582

Download citation

Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Lattice Site
  • Critical Probability