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On Network Structure Function Computations

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New Directions in Time Series Analysis

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 46))

Abstract

Some mathematical problems involving the asymptotic analysis of rooted random tree graphs and branching patterns for large numbers of vertices are described. The motivation comes from applications to hydrology and geomorphology in which one seeks formulae for the average behavior of various contours (level sets) associated with river networks and which depend on only a few large scale parameters. While this paper is mainly an overview, a new formula is derived in a special case as an illustration. Scaling problems and connections with Aldous’s new theory of “self-similar”continuum random trees are noted.

Department of Mathematics, Oregon State University, Corvallis, OR 97331. Research for this paper was partially supported by NSF grant DMS-8801466, ARO grant 27772-GS. The author gratefully acknowledges support from the Center for the Study of Earth from Space/CIRES and the Program in Applied Mathematics, University of Colorado, Boulder, CO 80309, during the final stages of preparation of this manuscript.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA

    Edward C. Waymire

Authors
  1. Edward C. Waymire
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Editor information

Editors and Affiliations

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

    David Brillinger

  2. Department of Electrical Engineering, McGill University, Montreal, Quebec, H3A 2A7, Canada

    Peter Caines

  3. Department of Economics, University of Minnesota, Minneapolis, MN, 55455, USA

    John Geweke

  4. Department of Statistics, Texas A&M University, College Station, TX, 77843-3143, USA

    Emanuel Parzen

  5. Mathematics Department, University of California, San Diego, La Jolla, CA, 92093, USA

    Murray Rosenblatt

  6. Department of Mathematics, Boston University, Boston, MA, 02215, USA

    Murad S. Taqqu

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© 1993 Springer-Verlag New York, Inc.

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Waymire, E.C. (1993). On Network Structure Function Computations. In: Brillinger, D., Caines, P., Geweke, J., Parzen, E., Rosenblatt, M., Taqqu, M.S. (eds) New Directions in Time Series Analysis. The IMA Volumes in Mathematics and its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9296-5_21

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  • DOI: https://doi.org/10.1007/978-1-4613-9296-5_21

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9298-9

  • Online ISBN: 978-1-4613-9296-5

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