NDLI: Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter

Content Provider	Springer Nature Link
Author	Forrester, Peter J. Rains, Eric M.
Copyright Year	2004
Abstract	A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the classical matrix ensembles with orthogonal symmetry, it is known that forming superpositions and decimations gives rise to classical matrix ensembles with unitary and symplectic symmetry. The basic identities expressing these facts can be extended to include a parameter, which in turn provides us with probability density functions which we take as the definition of special parameter dependent matrix ensembles. The parameter dependent ensembles relating to superpositions interpolate between superimposed orthogonal ensembles and a unitary ensemble, while the parameter dependent ensembles relating to decimations interpolate between an orthogonal ensemble with an even number of eigenvalues and a symplectic ensemble of half the number of eigenvalues. By the construction of new families of biorthogonal and skew orthogonal polynomials, we are able to compute the corresponding correlation functions, both in the finite system and in various scaled limits. Specializing back to the cases of orthogonal and symplectic symmetry, we find that our results imply different functional forms to those known previously.
Starting Page	518
Ending Page	576
Page Count	59
File Format	PDF
ISSN	01788051
Journal	Probability Theory and Related Fields
Volume Number	130
Issue Number	4
e-ISSN	14322064
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-07-05
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Biology in General Quantitative Finance Probability Theory and Stochastic Processes Mathematical and Computational Physics Statistics for Business/Economics/Mathematical Finance/Insurance Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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