- Home
- People
- Chief Investigators
- Peter Forrester
Professor Peter Forrester
The University of Melbourne
Peter Forrester received his Doctorate from the Australian National University in 1985, and held a postdoctoral position at Stony Brook before joining La Trobe University as a lecturer in 1987. In 1994 he was awarded a senior research fellowship by the ARC, which he took up at The University of Melbourne. Peter’s research interests are broadly in the area of mathematical physics, and more particularly in random matrix theory and related topics in statistical mechanics. This research and its applications motivated the writing of a large monograph Log-gases and Random Matrices (PUP, Princeton)which took place over a fifteen-year period. His research has been recognised by the award of the Medalof the Australian Mathematical Society in 1993, and election tothe Australian Academy of Science in 2004, in addition to several ARC personal fellowships. He was AustMS President from 2012 to 2014.
Qualifications:
PhD, Australian National University, 1986
Projects
Publications
Invited talks, refereed proceedings and other conference outputs
Forrester, P.
(2017). Random matrices Eurasia 2017.
Forrester, P.
(2017). PCMI Summer Session Random Matrices.
Forrester, P.
(2016). Random matrices: invariant measures, eigenvalue PDFS, integrals and characteristic polynomials, lecture 2.
Randomness in Physics and Mathematics.
Forrester, P.
(2016). Random matrices: invariant measures, eigenvalue PDFS, integrals and characteristic polynomials, lecture 1.
Randomness in Physics and Mathematics.
Forrester, P.
(2016). Invariant measures, volumes and random lattices.
Random matrices EurAsia 2016.
Forrester, P.
(2016). Invariant measures, volumes and random lattices.
JSIAM annual conference.
Forrester, P.
(2016). Dunkl theory in the study of random matrices.
Dunkl operators, special functions and harmonic analysis.
Forrester, P.
(2016). Random matrices: invariant measures, eigenvalue PDFS, integrals and characteristic polynomials, lecture 4.
Randomness in Physics and Mathematics.
Forrester, P.
(2016). Random matrices: invariant measures, eigenvalue PDFS, integrals and characteristic polynomials, lecture 3.
Randomness in Physics and Mathematics.
Journal Articles
Forrester, P., & Li S-H.
(2021). Fox H-kernel and $\theta $-deformation of the Cauchy Two-Matrix Model and Bures Ensemble.
International Mathematics Research Notices. 2021(8), 5791-5824. doi: 10.1093/imrn/rnz028
Forrester, P., & Li S-H.
(2020). Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions.
Transactions of the American Mathematical Society. 373, 665-698. doi: 10.1090/tran/7957
Forrester, P., & Zhang J.
(2020). Parametrising correlation matrices.
Journal of Multivariate Analysis. 178, doi: 10.1016/j.jmva.2020.104619
Forrester, P., & Trinh A. K.
(2019). Finite‐size corrections at the hard edge for the Laguerre β ensemble.
Studies in Applied Mathematics. 143(3), 315 - 336. doi: 10.1111/sapm.12279
Forrester, P., & Trinh A. K.
(2019). Optimal soft edge scaling variables for the Gaussian and Laguerre even β ensembles.
Nuclear Physics B. 938, 621 - 639. doi: 10.1016/j.nuclphysb.2018.12.006
Forrester, P., & Trinh A. K.
(2019). Comment on “Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices”.
Physical Review E. 99(3), 036101. doi: 10.1103/PhysRevE.99.036101
Forrester, P., & Ipsen J. R.
(2019). A generalisation of the relation between zeros of the complex Kac polynomial and eigenvalues of truncated unitary matrices.
Probability Theory and Related Fields. 175(3-4), 833 - 847. doi: 10.1007/s00440-019-00903-7
Forrester, P., Perk J. H. H., Trinh A. K., & Witte N. S.
(2019). Leading corrections to the scaling function on the diagonal for the two-dimensional Ising model.
Journal of Statistical Mechanics: Theory and Experiment. 2019(2), 023106. doi: 10.1088/1742-5468/ab00e6
Forrester, P., & Kumar S.
(2019). Recursion scheme for the largest $\beta$ -Wishart–Laguerre eigenvalue and Landauer conductance in quantum transport.
Journal of Physics A: Mathematical and Theoretical. 52(42), 42LT02. doi: 10.1088/1751-8121/ab433c
Forrester, P.
(2019). Volumes for $${\mathrm{SL}}_N({\mathbb {R}})$$ SL N ( R ) , the Selberg Integral and Random Lattices.
Foundations of Computational Mathematics. 19(1), 55 - 82. doi: 10.1007/s10208-018-9376-1
Forrester, P., Ipsen J. R., Liu D-Z., & Zhang L.
(2019). Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles.
Random Matrices: Theory and Applications. 8(4), 1950015. doi: 10.1142/S2010326319500151
Kieburg, M., Forrester P., & Ipsen J. R.
(2019). Multiplicative convolution of real asymmetric and real anti-symmetric matrices.
Advances in Pure and Applied Mathematics. 10(4), 467 - 492. doi: 10.1515/apam-2018-0037
Forrester, P.
(2019). Meet Andréief, Bordeaux 1886, and Andreev, Kharkov 1882–1883.
Random Matrices: Theory and Applications. 8(2), 1930001. doi: 10.1142/S2010326319300018
Forrester, P.
(2018). Comment on “Sum of squares of uniform random variables” by I. Weissman.
Statistics & Probability Letters. 142, 118 - 122. doi: 10.1016/j.spl.2018.04.020
Forrester, P., & Kumar S.
(2018). The Probability That All Eigenvalues are Real for Products of Truncated Real Orthogonal Random Matrices.
Journal of Theoretical Probability. 31(4), 2056 - 2071. doi: 10.1007/s10959-017-0766-0
Forrester, P., & Ipsen J.
(2018). Selberg integral theory and Muttalib–Borodin ensembles.
Advances in Applied Mathematics. 95, 152 - 176. doi: 10.1016/j.aam.2017.11.004
Forrester, P., Ipsen J., & Liu D-Z.
(2018). Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra–Itzykson–Zuber Integral.
Annales Henri Poincaré. 19(5), 1307 - 1348. doi: 10.1007/s00023-018-0654-x
Forrester, P., & Trinh A. K.
(2018). Functional form for the leading correction to the distribution of the largest eigenvalue in the GUE and LUE.
Journal of Mathematical Physics. 59(5), 053302. doi: 10.1063/1.5016347
Forrester, P., & Zhang J.
(2018). Volumes and distributions for random unimodular complex and quaternion lattices.
Journal of Number Theory. 190, 1 - 39. doi: 10.1016/j.jnt.2018.03.010
Forrester, P., Rahman A. A., & Witte N. S.
(2017). Large N expansions for the Laguerre and Jacobi β ensembles from the loop equations.
doi: 10.1063/1.4997778
Diaconis, P., & Forrester P.
(2017). Hurwitz and the origins of random matrix theory in mathematics.
Random Matrices: Theory and Applications. 06(01), 1730001. doi: 10.1142/S2010326317300017
Forrester, P.
(2017). Octonions in random matrix theory.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science. 473(2200), 20160800. doi: 10.1098/rspa.2016.0800
Bornemann, F., Forrester P., & Mays A.
(2017). Finite Size Effects for Spacing Distributions in Random Matrix Theory: Circular Ensembles and Riemann Zeros.
Studies in Applied Mathematics. 138(4), 401 - 437. doi: 10.1111/sapm.12160
Forrester, P., & Ipsen J.
(2016). Real eigenvalue statistics for products of asymmetric real Gaussian matrices.
Linear Algebra and its Applications. 510, 259-290. doi: 10.1016/j.laa.2016.08.015
Forrester, P., & Kieburg M.
(2016). Relating the Bures measure to the Cauchy two-matrix model.
Communications in Mathematical Physics. 342(1), 151-187. doi: 10.1007/s00220-015-2435-4
Forrester, P., & Grela J.
(2016). Hydrodynamical spectral evolution for random matrices.
Journal of Physics A: Mathematical and Theoretical. 49(8), doi: 10.1088/1751-8113/49/8/085203
Forrester, P.
(2016). Analogies between random matrix ensembles and the one-component plasma in two-dimensions.
Nuclear Physics B. 904, 253-281. doi: 10.1016/j.nuclphysb.2016.01.014
Forrester, P., & Liu D.
(2016). Singular values for products of complex Ginibre matrices with a source: Hard edge limit and phase transition.
Communications in Mathematical Physics. 344(1), 333-368. doi: 10.1007/s00220-015-2507-5
Bornemann, F., & Forrester P.
(2016). Singular values and evenness symmetry in random matrix theory.
Forum Mathematicum. 28(5), 873-891. doi: 10.1515/forum-2015-0055
Forrester, P., & Mays A.
(2015). Finite-size corrections in random matrix theory and Odlyzko’s dataset for the Riemann zeros.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science. 471(2182), 20150436. doi: 10.1098/rspa.2015.0436
Forrester, P., Liu D-Z., & Zinn-Justin P.
(2015). Equilibrium problems for Raney densities.
Nonlinearity. 28(7), 2265-2277. doi: 10.1088/0951-7715/28/7/2265
Forrester, P.
(2015). Asymptotics of finite system Lyapunov exponents for some random matrix ensembles.
Journal of Physics A: Mathematical and Theoretical. 48(21), 215205. doi: 10.1088/1751-8113/48/21/215205
Forrester, P.
(2015). Diffusion processes and the asymptotic bulk gap probability for the real Ginibre ensemble.
Journal of Physics A: Mathematical and Theoretical. 48(32), 324001. doi: 10.1088/1751-8113/48/32/324001
Witte, N. S., & Forrester P.
(2015). Loop equation analysis of the circular β ensembles.
Journal of High Energy Physics. 2015(2), doi: 10.1007/jhep02(2015)173
Can, T., Forrester P., Téllez G., & Wiegmann P.
(2014). Exact and Asymptotic Features of the Edge Density Profile for the One Component Plasma in Two Dimensions.
Journal of Statistical Physics. 158(5), 1147-1180. doi: 10.1007/s10955-014-1152-2
Forrester, P., & Lebowitz J. L.
(2014). Local Central Limit Theorem for Determinantal Point Processes.
Journal of Statistical Physics. 157(1), 60-69. doi: 10.1007/s10955-014-1071-2
