Toward a Solution to a Conjecture on Doubly Stochastic Eigenvalues [r-libre/4086]

Bouthat, Ludovick, Mashreghi, Javad et Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 (15 mai 2026). Toward a Solution to a Conjecture on Doubly Stochastic Eigenvalues. Communication (sur invitation) présentée au Seminar of mathematics at the University of Delaware, Newark, Delaware, États-Unis.

Fichier(s) associé(s) à ce document :

PDF - Beamer_Delaware.pdf
Contenu du fichier : Diaporama

Télécharger

Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Oui
Étape de publication :	Non publié
Résumé :	Stochastic matrices are matrices with nonnegative entries whose rows each sum to 1. When a matrix and its transpose are both stochastic, it is said to be doubly stochastic. In 1938, Kolmogorov proposed the problem of characterizing the region of possible eigenvalues of an n by n stochastic matrix, and Karpelevich gave a complete description thirteen years later. This talk concerns the doubly stochastic analogue: characterizing the region omega_n of eigenvalues of n by n doubly stochastic matrices, which is contained in the unit disk. Perfect and Mirsky (1965) conjectured that omega_n is the union of the regions Pi_k (the convex hulls of the k-th roots of unity) for k = 1,..., n. This conjecture holds for n = 1,2,3,4, but fails for n = 5. The case n greater or equal to 6 remains open. In response to the scarcity of progress over the past 60 years, Levick, Pereira, and Kribs proposed a related conjecture. In this talk, we propose an approach to a stronger version of this conjecture. The approach, based on majorization theory and geometric properties, also provides a potential general framework for characterizing omega_5, as well as a numerical method for testing the conjecture for various values of n.
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	25 mai 2026 13:53
Dernière modification :	11 aout 2026 11:59

Actions (connexion requise)

RÉVISER