Farid
Random Simplices : From Beta-Type Distributions to High-Dimensional Volumes
by Zakhar Kabluchko
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
ISBN: 3032028639 • Publisher: Springer Nature • Year: 2026
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
[color=#ff5555]📂 Category: Mathematics, Nonfiction
[color=#55acee]🌐 Language: English
[color=#44bb44]📄 Pages: 306
[color=#ff9900]📋 INFO: English | 2026 | ISBN: 3032028639 | 306 Pages | PDF EPUB (True) | 33 MB
[color=#888888]📝 DESCRIPTION: This book provides an introduction to the theory of random beta-type simplices and polytopes, exploring their connections to key research areas in stochastic and convex geometry. The random points defining the beta-type simplices, a class of random simplices introduced by Ruben and Miles, follow beta, beta-prime, or Gaussian distributions in the Euclidean space, and need not be identically distributed. A key tool in the analysis of these simplices, the so-called canonical decomposition, is presented here in a generalized form and is employed to derive explicit formulas for the moments of the volumes of beta-type simplices and to prove distributional representations for these volumes. Three independent approaches are described, including the original Ruben-Miles method. In addition, a version of the canonical decomposition for beta-type polytopes is provided, characterizing their typical faces as volume-weighted beta-type simplices. This is then applied to compute various expected functionals of beta-type polytopes, such as their volume, surface area and number of facets. The formulas for the moments of the volumes are also used to investigate several high-dimensional phenomena. Among these, a central limit theorem is established for the logarithmic volume of beta-type simplices in the high-dimensional limit. The canonical decomposition further motivates the study of beta-type distributions on affine Grassmannians, a subject to which the last chapter is dedicated.
[color=#ff9900]📦 Download Info
Folder: Random Simplices From Beta Type Distributions To High Dimensional Volumes
Format: EPUB
Total Size: 47.79 MB
📋 File List:
[size=2]
📌 Random Simplices.epub (Zakhar Kabluchko) (2026) (32.39 MB)
📌 Random Simplices.pdf (Zakhar Kabluchko) (2026) (14.4 MB)
————————————*****————————————
🔗NitroFlare
https://nitroflare.com/view/432906C5528D010/Random.Simplices.From.Beta.Type.Distributions.To.High.Dimensional.Volumes.rar?referrer=1635666
🔗RapidGator
https://rapidgator.net/file/1301576e51d8089271821ef4b5f8b594/Random.Simplices.From.Beta.Type.Distributions.To.High.Dimensional.Volumes.rar
