Spectral form factor in a random matrix theory
نویسندگان
چکیده
منابع مشابه
Spectral Form Factor in a Random Matrix Theory
In the theory of disordered systems the spectral form factor S(τ), the Fourier transform of the two-level correlation function with respect to the difference of energies, is linear for τ < τc and constant for τ > τc. Near zero and near τc its exhibits oscillations which have been discussed in several recent papers. In the problems of mesoscopic fluctuations and quantum chaos a comparison is oft...
متن کاملSpectral density of the correlation matrix of factor models: a random matrix theory approach.
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.
متن کاملFirst Colonization of a Spectral Outpost in Random Matrix Theory
We describe the distribution of the first finite number of eigenvalues in a newly-forming band of the spectrum of the random Hermitean matrix model. The method is rigorously based on the Riemann–Hilbert analysis of the corresponding orthogonal polynomials. We provide an analysis with an error term of order N−2γ where 1/γ = 2ν + 2 is the exponent of non-regularity of the effective potential, thu...
متن کاملSpectral rigidity of vehicular streams ( Random Matrix Theory approach )
Using the methods originally developed for Random Matrix Theory we derive an exact mathematical formula for number variance ∆N(L) (introduced in [4]) describing a rigidity of particle ensembles with power-law repulsion. The resulting relation is consequently compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of an inverse temper...
متن کاملUniversality in Random Matrix Theory
which is the Central Limit Theorem. In principle, all the random variables X1, X2, · · · , XN can be of order 1, hence SN ∼ 1 as well, but the probability of having such a rare event is incredibly small. We can even estimate the bound on the probability for the rare event from the large deviation principle. A similar phenomenon happens when we form a large matrix from i.i.d. random variables an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 1997
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.55.4067