Volumes for \(\text{SL}_N(\mathbb{R})\), the Selberg integral and random lattices

DOI10.1007/s10208-018-9376-1zbMath1446.11132arXiv1604.07462OpenAlexW2963635650MaRDI QIDQ1727977

Peter J. Forrester

Publication date: 21 February 2019

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.07462

zbMATH Keywords

random matricesgeometry of numberslattice reduction

Mathematics Subject Classification ID

Quotient spaces, decompositions in general topology (54B15) Geometry of numbers (11H99) Relations with random matrices (11M50)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the distribution of lengths of short vectors in a random lattice
• The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
• On the Poisson distribution of lengths of lattice vectors in a random lattice
• A Fuchsian matrix differential equation for Selberg correlation integrals
• The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates
• On the most compact regular lattices in large dimensions: A statistical mechanical approach
• Density of integer points on affine homogeneous varieties
• Singularity dominated strong fluctuations for some random matrix averages
• Average characteristic polynomials of determinantal point processes
• Diameters of random circulant graphs
• A mean value theorem in geometry of numbers
• Induced measures in the space of mixed quantum states
• How to pick a random integer matrix? (and other questions)
• Hurwitz and the origins of random matrix theory in mathematics
• On the distribution of angles between the N shortest vectors in a random lattice
• Universal microscopic correlation functions for products of independent Ginibre matrices
• Random matrix theory
• Kinetic transport in the two-dimensional periodic Lorentz gas
• The importance of the Selberg integral
• The $\bm{n}$-point correlations between values of a linear form
• Singular Value Statistics of Matrix Products with Truncated Unitary Matrices
• Generic Thinness in Finitely Generated Subgroups of SL$_n(\mathbb Z)$
• On the equidistribution of Hecke points
• Small solutions to linear congruences and Hecke equidistribution
• Algorithmic Number Theory
• The Asymptotic Value of the Volume of a Certain Set of Matrices
• The moments of the number of points of a lattice in a bounded set