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Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses
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  • Published: December 1992

Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses

  • A. Gandolfi1,
  • M. S. Keane2 &
  • C. M. Newman3 

Probability Theory and Related Fields volume 92, pages 511–527 (1992)Cite this article

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Summary

We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on ℤd or ℤd × ℕ with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on ℤd or on a slab ℤd × {0,...K} and prove both that percolation occurs and that the infinite component is unique forV=ℤ2×{0,1} or larger.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, CA, USA

    A. Gandolfi

  2. Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    M. S. Keane

  3. Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    C. M. Newman

Authors
  1. A. Gandolfi
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  2. M. S. Keane
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  3. C. M. Newman
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Additional information

A.G. was partially supported from AFOSR through grant no. 90-0090

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Gandolfi, A., Keane, M.S. & Newman, C.M. Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses. Probab. Th. Rel. Fields 92, 511–527 (1992). https://doi.org/10.1007/BF01274266

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  • Received: 06 July 1989

  • Revised: 26 November 1991

  • Issue Date: December 1992

  • DOI: https://doi.org/10.1007/BF01274266

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Random Graph
  • Spin Glass
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