Certain relations between correlations and statistics

Abstract

Correlation functions give a lot of information for the description of wavefields and for characters of media. We study the influence of correlations on the form of statistics of the model under consideration. The main points of such influence are the relations between correlations and the number of degrees of freedom of the model. The presence of correlations means certain reducing of full number of degrees of freedom, the absence of any correlations means that the system is realized over max value of degrees of freedom. That statement permits us to take into account the possible significance of phase space dimension (PSD) D of the system (the number of degrees of freedom of the system) on the form of partition function. The presence of correlations leads to the reducing of PSD D, and hence D might be treated as one of the fluctuating parameters in the procedure of deriving Gibbs partition function. Thus we present the partition function, that describes probability of realization for different values of PSD D and hence gives certain descriptions of the correlated behavior of our system. Simple cases and relations with the problems of wave propagation in random media are discussed.