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We study the integrable structure and scaling limits of the conditioned eigenvector overlap of the symplectic Ginibre ensemble of Gaussian non-Hermitian random matrices with independent quaternion elements. The average of the overlap matrix elements
Externí odkaz:
http://arxiv.org/abs/2407.17935
Autor:
Byun, Sung-Soo, Noda, Kohei
Non-Hermitian Wishart matrices were introduced in the context of quantum chromodynamics with a baryon chemical potential. These provide chiral extensions of the elliptic Ginibre ensembles as well as non-Hermitian extensions of the classical Wishart/L
Externí odkaz:
http://arxiv.org/abs/2402.18257
Autor:
Noda, Kohei
In this note, we study the determinantal structure of the $k$-th conditional expectation of the overlap for induced spherical unitary ensemble. We will show the universality for the scaling limits of the $k$-the conditional expectation of the overlap
Externí odkaz:
http://arxiv.org/abs/2312.12690
Let $\mathbf{W}\in\mathbb{C}^{n\times n}$ be a {\it single-spiked} Wishart matrix in the class $\mathbf{W}\sim \mathcal{CW}_n(m,\mathbf{I}_n+ \theta \mathbf{v}\mathbf{v}^\dagger) $ with $m\geq n$, where $\mathbf{I}_n$ is the $n\times n$ identity matr
Externí odkaz:
http://arxiv.org/abs/2110.11996
Autor:
Ameur, Yacin, Byun, Sung-Soo
We study the distribution of eigenvalues of almost-Hermitian random matrices associated with the classical Gaussian and Laguerre unitary ensembles. In the almost-Hermitian setting, which was pioneered by Fyodorov, Khoruzhenko and Sommers in the case
Externí odkaz:
http://arxiv.org/abs/2101.03832
Publikováno v:
Ann. Henri Poincar\'e. Volume 22 Issue 4 (2021) 1035-1068
We consider the complex eigenvalues of a Wishart type random matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$. For general
Externí odkaz:
http://arxiv.org/abs/2004.07626
Publikováno v:
Stat. Comput. 31 (2021) 7
We study sampling algorithms for $\beta$-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a random Ja
Externí odkaz:
http://arxiv.org/abs/2003.02344
Autor:
Dinh, Tien-Cuong, Vu, Duc-Viet
We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of Laguerre p
Externí odkaz:
http://arxiv.org/abs/1707.07174
Autor:
Deaño, Alfredo, Simm, Nick
In this paper, we compute the probability that an $N \times N$ matrix from the generalised Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dean and Majumdar \cite{DM}. For this purpose, we work out the large degr
Externí odkaz:
http://arxiv.org/abs/1610.08561
Autor:
Kornyik, Miklós, Michaletzky, György
In this paper we compute the leading terms in the sum of the $k^{th}$ power of the roots of $L_{p}^{(\alpha)}$, the Laguerre-polynomial of degree $p$ with parameter $\alpha$. The connection between the Laguerre-polynomials and the Marchenko-Pastur di
Externí odkaz:
http://arxiv.org/abs/1602.05001