Revisiting Horn’s problem Robert Coquereaux, Colin Mcswiggen, Jean-Bernard Zuber To cite this version: Robert Coquereaux, Colin Mcswiggen, Jean-Bernard Zuber. Revisiting Horn’s problem. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2019, Special Issue in Memory of Vladimir Rittenberg, 2019 (9), pp.094018. 10.1088/1742-5468/ab3bc2. hal-02418056 HAL Id: hal-02418056 https://hal.archives-ouvertes.fr/hal-02418056 Submitted on 15 Jan 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Revisiting Horn's Problem Robert Coquereaux Aix Marseille Univ, Universit´ede Toulon, CNRS, CPT, Marseille, France Colin McSwiggen:; and Jean-Bernard Zuber;˚ : Brown University, Division of Applied Mathematics, Providence, RI, USA z Sorbonne Universit´e,UMR 7589, LPTHE, F-75005, Paris, France & CNRS, UMR 7589, LPTHE, F-75005, Paris, France *
[email protected] Dedicated to the memory of Vladimir Rittenberg Abstract We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the classical case, we consider several generalizations in which the space of matrices under study carries an action of a compact Lie group, and the goal is to describe an associated probability measure on the space of orbits.