Octonions in random matrix theory

被引：1

作者：

Forrester, Peter J. ^{[1
]}

机构：

[1] Univ Melbourne, Dept Math & Stat, ARC Ctr Excellence Math & Stat Frontiers, Melbourne, Vic 3010, Australia

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2017年 / 473卷 / 2200期

基金：

澳大利亚研究理事会;

关键词：

random matrices; octonions; Jordan algebras; STATISTICAL THEORY; COMPLEX SYSTEMS; DYSON PROCESSES; ENERGY LEVELS; DISTRIBUTIONS; MODELS; CONES;

D O I：

10.1098/rspa.2016.0800

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random matrices by symmetry considerations. Only for N = 2 is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for N = 3. We then proceed to consider the matrix structure X+X, when X has random octonion entries. Analytic results are obtained from N = 2, but are observed to break down in the 3 x 3 case.

引用

页数：11

共 32 条

[11] Matrix models for beta ensembles [J].