Critical branching in a highly fluctuating random medium |
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Authors: | Donald A Dawson Klaus Fleischmann |
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Institution: | (1) Department of Mathematics and Statistics, Carleton University, K1S 5B6 Ottawa, Canada;(2) Karl Weierstrass Institute of Mathematics, Mohrenstrasse 39, O-1086 Berlin, Germany |
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Abstract: | Summary A model of one-dimensional critical branching (superprocess) is constructed in a random medium fluctuating both in time and space. The medium describes a moving system of point catalysts, and branching occurs only in the presence of these catalysts. Although the medium has an infinite overall density, the clumping features of the branching model can be exhibited by rescaling time, space, and mass by an exactly calculated scaling power which is stronger than in the constant medium case. The main technique used is the asymptotic analysis of a generalized diffusion-reaction equation in the space-time random medium, which (given the medium) prescribes the evolution of the Laplace transition functional of the Markov branching process. |
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