The Curie-Weiss Model with Dynamical External Field
2009, v.15, №1, 1-30
We study a Curie - Weiss model with a random external field generated by a dynamical system. Probabilistic limit theorems (weak law of large numbers, central limit theorems) are proven for the corresponding magnetization. Our results extend those already obtained in [R.S. Ellis,Entropy, Large Deviations and Statistical Mechanics, Springer-Verlag, New-York, 1985] and [R.S. Ellis and C.M. Newman, Limit theorems for sums of dependent random variables occuring in statistical mechanics, Z. Wahrsch. Verw. Geb., 1978, 44, 117-139].
Keywords: Curie - Weiss model,dynamic random walk,dynamical system,ergodic theory,diophantine approximations,limit theorems,large deviation principle,statistical physics