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pro vyhledávání: '"Forrester, Peter"'
The Gaussian and Laguerre orthogonal ensembles are fundamental to random matrix theory, and the marginal eigenvalue distributions are basic observable quantities. Notwithstanding a long history, a formulation providing high precision numerical evalua
Externí odkaz:
http://arxiv.org/abs/2411.15635
Autor:
Forrester, Peter J.
Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint eigenvalue
Externí odkaz:
http://arxiv.org/abs/2411.07356
Autor:
Forrester, Peter J.
The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations, most often
Externí odkaz:
http://arxiv.org/abs/2409.00964
The power spectrum is a Fourier series statistic associated with the covariances of the displacement from average positions of the members of an eigen-sequence. When this eigen-sequence has rotational invariance, as for the eigen-angles of Dyson's ci
Externí odkaz:
http://arxiv.org/abs/2408.15571
The eigenvalue probability density function of the Gaussian unitary ensemble permits a $q$-extension related to the discrete $q$-Hermite weight and corresponding $q$-orthogonal polynomials. A combinatorial counting method is used to specify a positiv
Externí odkaz:
http://arxiv.org/abs/2404.03400
Autor:
Forrester, Peter J., Kumar, Santosh
We consider the problem of the exact computation of the marginal eigenvalue distributions in the Laguerre and Jacobi $\beta$ ensembles. In the case $\beta=1$ this is a question of long standing in the mathematical statistics literature. A recursive p
Externí odkaz:
http://arxiv.org/abs/2402.16069
Autor:
Forrester, Peter J.
The paper "An efficient sampling scheme for the eigenvalues of dual Wishart matrices", by I.~Santamar\'ia and V.~Elvira, [\emph{IEEE Signal Processing Letters}, vol.~28, pp.~2177--2181, 2021] \cite{SE21}, poses the question of efficient sampling from
Externí odkaz:
http://arxiv.org/abs/2401.12409
Autor:
Byun, Sung-Soo, Forrester, Peter J.
The moments of the real eigenvalues of real Ginibre matrices are investigated from the viewpoint of explicit formulas, differential and difference equations, and large $N$ expansions. These topics are inter-related. For example, a third order differe
Externí odkaz:
http://arxiv.org/abs/2312.08896
Autor:
Forrester, Peter J.
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear differential e
Externí odkaz:
http://arxiv.org/abs/2309.09516
Autor:
Forrester, Peter J.
Publikováno v:
Tunisian J. Math. 6 (2024) 571-588
Generalised uncorrelated Wishart matrices are formed out of rectangular standard Gaussian data matrices with a certain pattern of zero entries. Development of the theory in the real and complex cases has proceeded along separate line. For example, em
Externí odkaz:
http://arxiv.org/abs/2308.15001