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pro vyhledávání: '"Forrester, A. J."'
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
Autor:
Forrester, Peter J., Shen, Bo-Jian
The family of circular Jacobi $\beta$ ensembles has a singularity of a type associated with Fisher and Hartwig in the theory of Toeplitz determinants. Our interest is in the Fourier transform of the corresponding bulk scaled spectral density about th
Externí odkaz:
http://arxiv.org/abs/2306.00525
Autor:
Forrester, Peter J.
Random matrices from the elliptic Ginibre orthogonal ensemble (GinOE) are a certain linear combination of a real symmetric, and real anti-symmetric, real Gaussian random matrices and controlled by a parameter $\tau$. Our interest is in the fluctuatio
Externí odkaz:
http://arxiv.org/abs/2305.09124