Skip to main content
SpringerLink
Log in

The Scaling Limit of Lattice Trees in High Dimensions

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract:

We prove that above eight dimensions the scaling limit of sufficiently spread-out lattice trees is the variant of super-Brownian motion known as integrated super-Brownian excursion (ISE), as conjectured by Aldous. The same is true for nearest-neighbour lattice trees in sufficiently high dimensions. The proof uses the lace expansion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada L8S 4K1.¶E-mail: slade@mcmaster.ca, , , , , , CA

    Eric Derbez & Gordon Slade

Authors
  1. Eric Derbez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gordon Slade
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 27 September 1996 / Accepted: 28 July 1997

Rights and permissions

Reprints and permissions

About this article

Cite this article

Derbez, E., Slade, G. The Scaling Limit of Lattice Trees in High Dimensions . Comm Math Phys 193, 69–104 (1998). https://doi.org/10.1007/s002200050319

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002200050319

Keywords

Search

Navigation