{"product_id":"random-simplices-von-zakhar-kabluchko-david-albert-steigenberger-und-christoph-thale","title":"Random Simplices","description":"\n                                \n                \u003cp\u003e\n                                        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.\n                    \n                    \u003cbr\u003e\n                                        \n                    \u003cbr\u003e\n                                        Largely 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.\n                \n                \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783032028631\"\u003e\u003ch3\u003eFrom Beta-Type Distributions to High-Dimensional Volumes\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783032028631","offer_id":57774874526021,"sku":"9783032028631","price":80.24,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/a2a7b3bf-f1f2-4589-920a-b6b0e6a09db7.jpg?v=1777090741","url":"https:\/\/shop.autorenwelt.de\/products\/random-simplices-von-zakhar-kabluchko-david-albert-steigenberger-und-christoph-thale","provider":"Autorenwelt Shop","version":"1.0","type":"link"}