Journal article

The Golden-Thompson inequality: Historical aspects and random matrix applications

Peter J Forrester, Colin J Thompson

JOURNAL OF MATHEMATICAL PHYSICS | AMER INST PHYSICS | Published : 2014

Abstract

The Golden-Thompson inequality, Tr (eA+B)≤ Tr (eAeB) for A, B Hermitianmatrices, appeared in independent works by Golden and Thompson published in 1965. Both of these were motivated by considerations in statistical mechanics. In recent years the Golden-Thompson inequality has found applications to random matrix theory. In this article, we detail some historical aspects relating to Thompson's work, giving in particular a hitherto unpublished proof due to Dyson, and correspondence with Pólya. We show too how the 2 × 2 case relates to hyperbolic geometry, and how the original inequality holds true with the trace operation replaced by any unitarily invariant norm. In relation to the random matri..

View full abstract

Grants

Funding Acknowledgements

The work of P.J.F. was supported by the Australian Research Council. We would also like to thank Freeman Dyson for encouraging correspondence and for allowing us to reproduce the proof of his ingenious Lemma 2.