Summary
A critical branching random walk in a d-dimensional spatial random medium (environment) is considered. It is said to be “persistent” if there is no loss of particle intensity in the large time limit. A critical dimension d c is shown to exist such that the system is persistent if d>d c and fails to be persistent if d<d c.
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Research supported by the Natural Sciences and Engineering Research Council of Canada
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Dawson, D.A., Fleischmann, K. Critical dimension for a model of branching in a random medium. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 315–334 (1985). https://doi.org/10.1007/BF00534864
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DOI: https://doi.org/10.1007/BF00534864