P. Forrester

activity

19942023

τ

-Function Theory of Painlevé Equations to Random Matrices: PIV, PII and the GUE

193 citations · 2.8k across the 159 of their papers we have counts for

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math-ph2003★ 16 cited

Growth models, random matrices and Painleve transcendents

Peter J. Forrester

The Hammersley process relates to the statistical properties of the maximum length of all up/right paths connecting random points of a given density in the unit square from (0,0) t…

math-ph2003

Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and $N$ -recurrences for averages over U(N) -- \PVI $τ$ -functions

P. J. Forrester, N. S. Witte

The theory of orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials an…

math-ph2003

Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and N-recurrences for averages over U(N) -- \PIIIa and \PV $τ$ -functions

P. J. Forrester, N. S. Witte

In this work we show that the $N \times N$ Toeplitz determinants with the symbols $z^{μ} exp (- 1/2 t (z + 1/ z))$ and $(1 + z)^{μ} (1 + 1/ z)^{ν} exp (t z)$ -- known $τ$ -functions for th…

Growth models, random matrices and Painleve transcendents

Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and N-recurrences for averages over U(N) -- \PVI τ-functions

Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and N-recurrences for averages over U(N) -- \PIIIa and \PV τ-functions

Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and $N$ -recurrences for averages over U(N) -- \PVI $τ$ -functions

Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and N-recurrences for averages over U(N) -- \PIIIa and \PV $τ$ -functions