Large deviations of the smallest eigenvalue of the Wishart-Laguerre ensemble.
نویسندگان
چکیده
We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our results are compared with known exact results for β=1 finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.
منابع مشابه
Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations
Let λ1, · · · , λn be random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n, p). In the case that the sample size n is much smaller than the dimension of the population distribution p, a common situation in modern data, we approximate the beta-Laguerre ensemble by a beta-Hermite ...
متن کاملOn the condition number of the critically-scaled Laguerre Unitary Ensemble
We consider the Laguerre Unitary Ensemble (aka, Wishart Ensemble) of sample covariance matrices A = XX∗, where X is an N × n matrix with iid standard complex normal entries. Under the scaling n = N + b √ 4cNc, c > 0 and N →∞, we show that the rescaled fluctuations of the smallest eigenvalue, largest eigenvalue and condition number of the matrices A are all given by the Tracy–Widom distribution ...
متن کاملThe 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 کاملPainlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles
The scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles is evaluated in terms of a Painlevé V transcendent. This same Painlevé V transcendent is known from the work of Tracy and Widom, where it has been shown to specify the scaled distribution of the smallest eigenvalue in the Laguerre unitary ensemble. The starting point for our calculation is the...
متن کاملAsymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles
We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble (MANOVA). If n is the size of the sample, r ≤ n the number of variates and Xn,r such a matrix, a generalization of the Bartlett-type theorems gives a decomposi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 82 4 Pt 1 شماره
صفحات -
تاریخ انتشار 2010