Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Simm, Nick"'
Autor:
Simm, Nick, Wei, Fei
We consider the derivative of the characteristic polynomial of $N \times N$ Haar distributed unitary matrices. In the limit $N \to \infty$, we give a formula for general non-integer moments of the derivative for values of the spectral variable inside
Externí odkaz:
http://arxiv.org/abs/2409.03687
Autor:
Serebryakov, Alexander, Simm, Nick
We study $k$-point correlators of characteristic polynomials in non-Hermitian ensembles of random matrices, focusing on the real, complex and quaternion $N \times N$ Ginibre ensembles. Our approach is based on the technique of character expansions, w
Externí odkaz:
http://arxiv.org/abs/2310.20686
We study real eigenvalues of $N\times N$ real elliptic Ginibre matrices indexed by a non-Hermiticity parameter $0\leq \tau<1$, in both the strong and weak non-Hermiticity regime. Here $N$ is assumed to be an even number. In both regimes, we prove a c
Externí odkaz:
http://arxiv.org/abs/2305.02753
We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argume
Externí odkaz:
http://arxiv.org/abs/2109.10331
Autor:
FitzGerald, Will, Simm, Nick
We study the real eigenvalue statistics of products of independent real Ginibre random matrices. These are matrices all of whose entries are real i.i.d. standard Gaussian random variables. For such product ensembles, we demonstrate the asymptotic nor
Externí odkaz:
http://arxiv.org/abs/2109.00322
Let $O$ be chosen uniformly at random from the group of $(N+L) \times (N+L)$ orthogonal matrices. Denote by $\tilde{O}$ the upper-left $N \times N$ corner of $O$, which we refer to as a truncation of $O$. In this paper we prove two conjectures of For
Externí odkaz:
http://arxiv.org/abs/2102.08842
We study the secular coefficients of $N \times N$ random unitary matrices $U_{N}$ drawn from the Circular $\beta$-Ensemble, which are defined as the coefficients of $\{z^n\}$ in the characteristic polynomial $\det(1-zU_{N}^{*})$. When $\beta > 4$ we
Externí odkaz:
http://arxiv.org/abs/2011.01823
Akademický článek
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Autor:
Deaño, Alfredo, Simm, Nick
Publikováno v:
International Mathematics Research Notices, rnaa111 (2020)
We study expectations of powers and correlation functions for characteristic polynomials of $N \times N$ non-Hermitian random matrices. For the $1$-point and $2$-point correlation function, we obtain several characterizations in terms of Painlev\'e t
Externí odkaz:
http://arxiv.org/abs/1909.06334
Publikováno v:
Commun. Math. Phys. 369(3), 1091-1145 (2019)
We establish a new connection between moments of $n \times n$ random matrices $X_n$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s \in \mathbb{C}$
Externí odkaz:
http://arxiv.org/abs/1805.08760