ИСТИНА

In Introduction we describe the maim steps in development of the central limit theorem for independent random variables. After that we concentrate on the dependence conditions for random field. Special attention is paid to the Newman conjecture. Then it is shown how to modify this conjecture and to establish necessary and sufficient conditions for the CLT validity for a class of random fields. Among various applications we demonstrate the CLT for the excursion sets volumes. Convergence rates estimates in the CLT are discussed as well.