First colonization of a hard-edge in random matrix theory
نویسندگان
چکیده
We describe the spectral statistics of the first finite number of eigenvalues in a newly-forming band on the hardedge of the spectrum of a random Hermitean matrix model. It is found that in a suitable scaling regime, they are described by the same spectral statistics of a finite-size Laguerre-type matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding orthogonal polynomials.
منابع مشابه
Diffusion at the random matrix hard edge
We show that the limiting minimal eigenvalue distributions for a natural generalization of Gaussian sample-covariance structures (the “beta ensembles”) are described by the spectrum of a random diffusion generator. By a Riccati transformation, we obtain a second diffusion description of the limiting eigenvalues in terms of hitting laws. This picture pertains to the so-called hard edge of random...
متن کاملAPPLICATION OF THE RANDOM MATRIX THEORY ON THE CROSS-CORRELATION OF STOCK PRICES
The analysis of cross-correlations is extensively applied for understanding of interconnections in stock markets. Variety of methods are used in order to search stock cross-correlations including the Random Matrix Theory (RMT), the Principal Component Analysis (PCA) and the Hierachical Structures. In this work, we analyze cross-crrelations between price fluctuations of 20 company stocks...
متن کاملUniversality Limits at the Hard Edge of the Spectrum for Measures with Compact Support
We use the theory of entire functions and reproducing kernels to establish universality at the (hard) edge of the spectrum for a measure with compact support. This involves the Bessel kernel. In particular, we show that universality at the hard edge is equivalent to universality along the diagonal at the hard edge. 1. Results Let be a nite positive Borel measure with compact support supp[ ]. T...
متن کاملFree vibration and buckling analysis of third-order shear deformation plate theory using exact wave propagation approach
In this paper, wave propagation approach is used to analysis the free vibration and buckling analysis of the thick rectangular plates based on higher order shear deformation plate theory. From wave viewpoint, vibrations can be considered as traveling waves along structures. Waves propagate in a waveguide and reflect at the boundaries. It is assumed that the plate has two opposite edge simply su...
متن کاملDensity and Polarization Profiles of Dipolar Hard Ellipsoids Confined between Hard Walls: A Density Functional Theory Approach
The density and polarization profiles of the dipolar hard ellipsoids confined between hard walls are studied using the density functional theory (DFT). The Hyper-Netted Chain (HNC) approximation is used to write excess grand potential of the system with respect to the bulk value. The number density is expanded up to zero and first order in polarization to find the results. For the zero order in...
متن کامل