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Segmentation and Filtering into Neighborhoods as Processes of Percolation and Diffusion: Stochastic Processes (Randomness) as the Null Hypothesis

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  • M H Krieger

    (School of Urban and Regional Planning, University of Southern California, Los Angeles, CA 90089-0042, USA)

Abstract

A set of models is reviewed in which orderly urban phenomena are accounted for in terms of noise (randomness, stochastic processes): segmentation as a process of runs in random processes (percolation); filtering as a process of random walk and so diffusion, and as a Markov process. In particular, ‘continuity’ of the spatial price envelope, a truism of real estate, leads to the diffusion equation. No foreordained centers, boundaries, or gravity (or entropy) is needed to obtain clustering in these models. The models are combined in a simulation, implemented in a Lotus 1-2-3 spreadsheet, as well as in a partial differential equation driven by a stochastic source term.

Suggested Citation

  • M H Krieger, 1991. "Segmentation and Filtering into Neighborhoods as Processes of Percolation and Diffusion: Stochastic Processes (Randomness) as the Null Hypothesis," Environment and Planning A, , vol. 23(11), pages 1609-1626, November.
    • Handle: RePEc:sae:envira:v:23:y:1991:i:11:p:1609-1626
    DOI: 10.1068/a231609
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    References listed on IDEAS

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    1. Arthur, W Brian, 1989. "Competing Technologies, Increasing Returns, and Lock-In by Historical Events," Economic Journal, Royal Economic Society, vol. 99(394), pages 116-131, March.
    2. Berger,Suzanne & Piore,Michael J., 1980. "Dualism and Discontinuity in Industrial Societies," Cambridge Books, Cambridge University Press, number 9780521231343.
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    Cited by:

    1. Yiming Wang, 2012. "Decomposing the entropy index of racial diversity: in search of two types of variance," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 48(3), pages 897-915, June.

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