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Interpretations of some parameter dependent generalizations of classical matrix ensembles
Peter J. Forrester, Eric M. Rains
Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolat…
Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter
Peter J. Forrester, Eric M. Rains
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…
Dynamical Correlations for Circular Ensembles of Random Matrices
Taro Nagao, Peter J. Forrester
Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitar…
Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable Bosons
P. J. Forrester, N. E. Frankel, T. M. Garoni +1
The recent experimental realisation of a one-dimensional Bose gas of ultra cold alkali atoms has renewed attention on the theoretical properties of the impenetrable Bose gas. Of pr…
Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
Alexei Borodin, Peter J. Forrester
Our interest is in the cumulative probabilities Pr(L(t) \le l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point…
Application of the -function theory of Painlevé equations to random matrices: \PVI, the JUE, CyUE, cJUE and scaled limits
P. J. Forrester, N. S. Witte
Okamoto has obtained a sequence of -functions for the \PVI system expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting…