The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on low-dimensional (quasi-1D and 2D) systems. Calculations are based on the supermatrix σ-model approach. The method reproduces, in so-called zero-mode approximation, the uni...

In this paper we presented an extension of previous results given in the papers [15], [17],[19], main idea proofs is: write down difference trigonometric kernel general expansion considered, and have to estimate resulting infinite sums. For terms these sums used sharper different estimates than literature (the most exact where by V.A.Il’n, I. Joó V.Komornik).