The large-scale structure of the universe and quasi-Voronoi tessellation of shock fronts in forced Burgers turbulence in \boldR\spd

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 Rd 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.