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We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues ${x_j}_{j=1}^N$ are close to their classical location ${\gamma_j}_{j=1}^N$ determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/N, the necessary apriori estimate on the location of eigenvalues requires only to know that $\E |x_j - \gamma_j |^2 \le N^{-1-\e}$ on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for Wishart matrices.

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In an infinite sequence of independent identically distributed continuous random variables we study the number of strings of two subsequent records interrupted by a given number of non-records. By embedding in a marked Poisson process we prove that these counts are independent and Poisson distributed. Also the distribution of the number of uninterrupted strings of records is considered.

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