A Complete solution to a conjecture on doubly stochastic eigenvalues [r-libre/4086]

Bouthat, Ludovick, Mashreghi, Javad et Morneau-Guérin, Frédéric (15 May 2026). A Complete solution to a conjecture on doubly stochastic eigenvalues. Paper (invited) presented at the Analysis seminar, Newark, Delaware, États-Unis.

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Item Type:	Conference papers (unpublished)
Refereed:	Yes
Status:	Unpublished
Abstract:	This talk surveys recent advances on a classical spectral problem concerning doubly stochastic matrices. While Karpelevič completely characterized the possible eigenvalues of stochastic matrices in 1951, the analogous problem for doubly stochastic matrices, posed by Mirsky in 1963, remains only partially understood. After reviewing the Perfect-Mirsky conjecture and its surprising failure in dimension five, we present a new geometric approach based on families of convex polygons associated with eigenvectors and their invariance properties under multiplication by eigenvalues. We then discuss recent joint work establishing that eigenvalues associated with convexly independent eigenvectors must lie in a much smaller region than previously expected, together with the dynamical and circulant-matrix methods underlying the proof. Finally, we describe consequences for the structure of the known counterexamples and discuss heuristics and numerical evidence suggesting that the conjecture may nevertheless hold in dimensions n greater or equal to 6.
Depositor:	Morneau-Guérin, Frédéric
Owner / Manager:	Frédéric Morneau-Guérin
Deposited:	25 May 2026 13:53
Last Modified:	25 May 2026 13:53

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