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Perplexing Problems in Probability pp 35–51Cite as

Lattice Trees, Percolation and Super-Brownian Motion

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Part of the book series: Progress in Probability ((PRPR,volume 44))

Abstract

This paper surveys the results of recent collaborations with Eric Derbez and with Takashi Hara, which show that integrated super-Brownian excursion (ISE) arises as the scaling limit of both lattice trees and the incipient infinite percolation cluster, in high dimensions. A potential extension to oriented percolation is also mentioned.

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Author information

Author notes

  1. Gordon Slade

    Present address: Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z2

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada, L8S 4K1

    Gordon Slade

Authors
  1. Gordon Slade
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Maury Bramson

  2. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Rick Durrett

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© 1999 Birkhäuser Boston

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Slade, G. (1999). Lattice Trees, Percolation and Super-Brownian Motion. In: Bramson, M., Durrett, R. (eds) Perplexing Problems in Probability. Progress in Probability, vol 44. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2168-5_2

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  • DOI: https://doi.org/10.1007/978-1-4612-2168-5_2

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7442-1

  • Online ISBN: 978-1-4612-2168-5

  • eBook Packages: Springer Book Archive

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