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February 1997 The large-scale structure of the universe and quasi-Voronoi tessellation of shock fronts in forced Burgers turbulence in $\bold R\sp {d}$
S. A. Molchanov, D. Surgailis, W. A. Woyczynski
Ann. Appl. Probab. 7(1): 200-228 (February 1997). DOI: 10.1214/aoap/1034625260

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.

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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

Information

Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0895.60066
MathSciNet: MR1428757
Digital Object Identifier: 10.1214/aoap/1034625260

Subjects:
Primary: 60H15
Secondary: 35Q53 , 60G60 , 60K40 , 70K40 , 76L05 , 83F05

Keywords: Forced Burgers turbulence , large-scale structure of the Universe , quasi-Voronoi tessellations

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 1 • February 1997
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