Výsledky vyhledávání

Report

Central limit theorems for the real eigenvalues of large Gaussian random matrices

Autor: Simm, N. J.

Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system consisting of pure

Externí odkaz: http://arxiv.org/abs/1512.01449

Zobrazit plný text záznamu

Report

Mesoscopic linear statistics of Wigner matrices

Autor: Lodhia, A., Simm, N. J.

We study linear spectral statistics of $N \times N$ Wigner random matrices $\mathcal{H}$ on mesoscopic scales. Under mild assumptions on the matrix entries of $\mathcal{H}$, we prove that after centering and normalizing, the trace of the resolvent $\

Externí odkaz: http://arxiv.org/abs/1503.03533

Zobrazit plný text záznamu

Report

Fractional Brownian motion with Hurst index $H=0$ and the Gaussian Unitary Ensemble

Autor: Fyodorov, Y. V., Khoruzhenko, B. A., Simm, N. J.

Publikováno v: Annals of Probability 2016, Vol. 44, No. 4, 2980-3031

The goal of this paper is to establish a relation between characteristic polynomials of $N\times N$ GUE random matrices $\mathcal{H}$ as $N\to\infty$, and Gaussian processes with logarithmic correlations. We introduce a regularized version of fractio

Externí odkaz: http://arxiv.org/abs/1312.0212

Zobrazit plný text záznamu

Report

Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4

Autor: Mezzadri, F., Simm, N. J.

Publikováno v: Commun. Math. Phys, Vol. 324, 465-513 (2013)

We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and appl

Externí odkaz: http://arxiv.org/abs/1206.4584

Zobrazit plný text záznamu

Report

Moments of the transmission eigenvalues, proper delay times and random matrix theory II

Autor: Mezzadri, F., Simm, N. J.

Publikováno v: J. Math. Phys., Vol. 53 (2012), 053504

We systematically study the first three terms in the asymptotic expansions of the moments of the transmission eigenvalues and proper delay times as the number of quantum channels n in the leads goes to infinity. The computations are based on the assu

Externí odkaz: http://arxiv.org/abs/1108.2859

Zobrazit plný text záznamu