2004/06/21 by Leonid Gurvits, Gurvits, Leonid
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Point processes and geometric inequalities #Statistical Methods and Inference #math.CO
paper · pdf · doi:10.48550/arxiv.math/0406420
18 pages
arxiv created 2004/06/21 · openalex publication_date 2004/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the mixed discriminant of doubly stochastic n-tuples of semidefinite hermitian n × n matrices is bounded below by \fracn!nn and that this bound is uniquely attained at the n-tuple ((1)/(n) I,...,(1)/(n) I). This result settles a conjecture posed by R. Bapat in 1989. We consider various generalizations and applications of this result.