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.

Consider $N\times N$ Hermitian or symmetric random matrices $H$ where the distribution of the $(i,j)$ matrix element is given by a probability measure $\nu_{ij}$ with a subexponential decay. Let $\sigma_{ij}^2$ be the variance for the probability measure $\nu_{ij}$ with the normalization property that $\sum_{i} \sigma^2_{ij} = 1$ for all $j$. Under essentially the only condition that $c\le N \sigma_{ij}^2 \le c^{-1}$ for some constant $c>0$, we prove that, in the limit $N \to \infty$, the eigenvalue spacing statistics of $H$ in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth $M$ the local semicircle law holds to the energy scale $M^{-1}$.

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For Komatu-Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of \cite{S} to find the SDEs satisfied by the induced motion $\xi(t)$ on $\partial\HH$ and the slit motion $\s(t)$. The diffusion coefficient $\alpha$ and drift coefficient $b$ of such SDEs are homogenous functions. Next with solutions of such SDEs, we study the corresponding stochastic Komatu-Loewner evolution, denoted as ${\rm SKLE}_{\alpha,b}$. We introduce a function $b_{\rm BMD}$ measuring the discrepancy of a standard slit domain from $\HH$ relative to BMD. We show that ${\rm SKLE}_{\sqrt{6},-b_{\rm BMD}}$ enjoys a locality property.