2008/04/24 by Andrea Gabrielli, Gabrielli, Andrea, Fabio Cecconi +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Physical sciences #Financial Risk and Volatility Modeling #Statistical Mechanics (cond-mat.stat-mech) #Statistical Methods and Bayesian Inference #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0804.3912
IOP-LaTeX, 17 pages J. Phys. A: Theor. Mat. 2008 in press
arxiv created 2008/04/24 · openalex publication_date 2008/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the dynamics of the two-point statistics of the Kraichnan ensemble which describes the transport of a passive pollutant by a stochastic turbulent flow characterized by scale invariant structure functions. The fundamental equation of this problem consists in the Fokker-Planck equation for the two-point correlation function of the density of particles performing spatially correlated Brownian motions with scale invariant correlations. This problem is equivalent to the stochastic motion of an effective particle driven by a generic multiplicative noise. In this paper we propose an alternative and more intuitive approach to the problem than the original one leading to the same conclusions. The general features of this new approach make possible to fit it to other more complex contexts.