2019/06/14 by Bero Roos, Roos, Bero · 1 citation
Mathematics · #15A15 #15A45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Graph theory and applications #Point processes and geometric inequalities #Random Matrices and Applications #math.CA #msc:15A15 #msc:15A45
paper · pdf · doi:10.48550/arxiv.1906.06176
34 pages. Introduction and literature enlarged; Corollary 1.1 of version 1 is changed to Theorem 1.1 of version 2; application to random diagonal sums and numerical comparison of permanental bounds included (see the new Sections 1.4 and 1.5)
openalex publication_date 2019/06/14 · arxiv created 2020/05/10 · arxiv updated 2020/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show new upper bounds for permanents and hafnians, which are particularly useful for complex matrices. Multidimensional permanents and hyperhafnians are considered as well. The permanental bounds improve on a Hadamard type inequality of Carlen, Lieb and Loss (2006, Methods and Applications of Analysis 13, 1--17) and Cobos, Kühn and Peetre (2006, Integral Equations and Operator Theory 56, 57--70). Our proofs are based on a more general inequality, which can be applied to generalized Laplace type expansions of the matrix functions under consideration. As application, we show new bounds on the characteristic function of random diagonal sums. A numerical comparison shows the performance of some of our permanental bounds.