Complete Asymptotic Expansions for the Normalizing Constants of High-Dimensional Matrix Bingham and Matrix Langevin Distributions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Bagyan, Armine, Richards, Donald
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212652
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Complete Asymptotic Expansions for the Normalizing Constants of High-Dimensional Matrix Bingham and Matrix Langevin Distributions. Armine Bagyan and Donald Richards. SIGMA 20 (2024), 094, 22 pages

For positive integers and p such that ≥ , let ℝᵈˣᵖ denote the set of × real matrices, ₚ be the identity matrix of order , and d,ₚ = { ∈ ℝᵈˣᵖ ∣ ′ = ₚ} be the Stiefel manifold in ℝᵈˣᵖ. Complete asymptotic expansions as → ∞ are obtained for the normalizing constants of the matrix Bingham and matri...