Anderson Parabolic Model for a Quasi-Stationary Medium
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We study the Anderson Parabolic Model for a random medium which is a product of an i.i.d. space-like random field and a white noise. The model has long range space-time correlations and is intermediate between the stationary case and the “turbulent” one, which were studied in previous works. Under some natural assumptions on the distribution of the space potential, we prove existence and uniqueness, and derive the long time asymptotics for the annealed moments, and the “semi-annealed” ones, for which expectation is taken only w.r.t. the white noise. A conjecture for the fully quenched case is discussed on a simplified model.
KeywordsRandom Walk White Noise Weibull Distribution Stat Phys Random Medium
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- 3.Zeldovich, Ya., Molchanov, S., Ruzmaikin, A., Sokolov, D.: Intermittency, Diffusion and Generation in a Non-Stationary Random Medium. Russian Reviews in Mathematical Physics. Cambridge University Press, Cambridge (1989) Google Scholar
- 4.Carmona, R., Molchanov, S.A.: Parabolic Anderson problem and intermittency. Mem. Am. Math. Soc. 108, 518 (1994) Google Scholar
- 5.Molchanov, S.: Lectures on Random Media. In: Bernard, P. (ed.) Lectures in Probability Theory, Ecole d’ Eté de Probabilités de Saint Flour XXII, 1992. Lecture Notes in Mathematics, vol. 1581, pp. 242–411. Springer, Berlin (1994) Google Scholar