Abstract
An important astrophysical problem about the generation of a magnetic field ⃗ H(t, x) by a turbulent flow of electrically conducting plasma with a random velocity field stationary in time and space was considered in (semi)physical works (see [1] and, in particular, the review paper [2]).However, in these papers only the second moments of the field ⃗ H(t, x) (correlation functions) were studied.In a highly simplified scalar problem (the Anderson model with a white noise type potential; see [3]) the highest Lyapunov exponents and sample (P-almost surely) Lyapunov exponent were found as functions of the magnetic viscosity of the medium.The goal of this paper is to realize a similar program for the vector field ⃗ H(t, x) but in discrete space-time.Such a simplification is technically convenient, but retains all the qualitative features of the problem.