The norm of infinite doubly stochastic matrices [r-libre/4185]

Bouthat, Ludovick, Mashreghi, Javad et Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 (04 aout 2026). The norm of infinite doubly stochastic matrices. Communication (sur invitation) présentée à International Workshop on Operator Theory and its Applications (IWOTA) 2026, Québec.

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Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Non
Étape de publication :	Non publié
Résumé :	In finite dimensions, every doubly stochastic matrix has an l^p-operator norm equal to 1 for all p greater or equal to 1 (and possibly infinite). However, in the infinite-dimensional setting, this property may fail since its norm can be strictly smaller than 1 when p is finite and strictly greater than 1. In this talk, we provide an elegant characterization of infinite doubly stochastic matrices for which the norm remains equal to 1 is obtained. More precisely, we show that the norm is equal to 1 precisely when the matrix contains arbitrarily large finite regions in which it behaves ``almost'' like a finite doubly stochastic matrix. The proof uses a Cheeger-type argument, highlighting a natural connection with ideas from spectral graph theory.
Adresse de la version officielle :	https://iwota-2026.fsg.ulaval.ca/
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	11 aout 2026 18:20
Dernière modification :	14 aout 2026 14:14

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