Abstract
Burgers turbulence is an accepted formalism for the adhesion model of the large-scale distribution of matter in the universe. The paper uses variational methods to establish evolution of quasi-Voronoi (curved boundaries) tessellation structure of shock fronts for solutions of the inviscid nonhomogeneous Burgers equation in $R^d$ in the presence of random forcing due to a degenerate potential. The mean rate of growth of the quasi-Voronoi cells is calculated and a scaled limit random tessellation structure is found. Time evolution of the probability that a cell contains a ball of a given radius is also determined.
Citation
S. A. Molchanov. D. Surgailis. W. A. Woyczynski. "The large-scale structure of the universe and quasi-Voronoi tessellation of shock fronts in forced Burgers turbulence in $\bold R\sp {d}$." Ann. Appl. Probab. 7 (1) 200 - 228, February 1997. https://doi.org/10.1214/aoap/1034625260
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