A smooth transition from Wishart to GOE
نویسندگان
چکیده
It is well known that an n × n Wishart matrix with d degrees of freedom is close to the appropriately centered and scaled Gaussian Orthogonal Ensemble (GOE) if d is large enough. Recent work of Bubeck, Ding, Eldan, and Racz, and independently Jiang and Li, shows that the transition happens when d = Θ(n). Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when d/n → c ∈ (0,∞). This shows, in particular, that the phase transition from Wishart to GOE is smooth.
منابع مشابه
The Largest Sample Eigenvalue Distribution in the Rank 1 Quaternionic Spiked Model of Wishart Ensemble
We solve the largest sample eigenvalue distribution problem in the rank 1 spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge. We observe a phase change phenomenon similar to that in the complex case, and prove that the new distribution at the phase change point is the GOE Tracy-Wid...
متن کاملLevel density for deformations of the Gaussian orthogonal ensemble.
Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles, we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to m GOEs.
متن کاملDistribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also found that the Tracy-Widom law can be approximated by a properly scaled and shifted gamma distribution, with...
متن کاملAsymmetric Behavior of Inflation in Iran: New Evidence on Inflation Persistence Using a Smooth Transition Model
T his paper investigates the asymmetric behavior of inflation. We use logistic smooth transition autoregressive (LSTAR) model to characterize the regime-switching behavior of Iran’s monthly inflation during the period May 1990 to December 2013. We find that there is a triple relationship between the inflation level, its fluctuations and persistence. The findings imply that the behavi...
متن کاملThe bulk and edge spectra of critical values of smooth isotropic processes
We study the behaviour of the critical values of smooth isotropic processes, which we consider as a generalization of the eigenvalues of random matrices. Isotropic processes on R, invariant under rigid motions of R, have a large symmetry group as do the classical random matrix ensembles, with the GOE ensemble being the most relevant. We discuss in what ways the critical values of an isotropic p...
متن کامل