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Gibbs-Cox random fields and Burgers turbulence. (English) Zbl 0838.60016

The functionals on shot-noise fields with spatial distribution driven by the Gibbs-Cox field are studied. This permits to establish the non-Gaussian scaling limits for the solutions of Burger’s equation with shot-noise type initial data mentioned above. It provides a generalization of previous results in this direction. Connections with other related investigations by mathematicians and physicists and possible applications are discussed.

MSC:

60F05 Central limit and other weak theorems
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76F20 Dynamical systems approach to turbulence
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