{"product_id":"9783032028631","title":"Lecture Notes in Mathematics: From Beta-Type Distributions to High-Dimensional Volumes","description":"\u003ch1\u003eLecture Notes in Mathematics: From Beta-Type Distributions to High-Dimensional Volumes\u003c\/h1\u003e \u003ch2\u003eKabluchko, Zakhar; Steigenberger, David Albert; Thäle, Christoph\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003cbr\u003e\u003cbr\u003eLargely self-contained, requiring minimal prior knowledge, the book connects these topics to a broad range of past and current research, serving as an excellent resource for graduate students and researchers seeking to engage with the field of stochastic and integral geometry.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2026-04-02\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783032028631\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-032-02864-8\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 300\u003c\/p\u003e ","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":44309069561996,"sku":"9783032028631","price":76.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032028631.jpg?v=1777373429","url":"https:\/\/lateknightbooks.com\/products\/9783032028631","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}