@phdthesis{Juhos2024, author = {Juhos, Michael}, title = {Probabilistic and geometric aspects of classical and non-commutative lp-type spaces in high dimensions}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus4-14857}, school = {Universit{\"a}t Passau}, pages = {viii, 157 Seiten}, year = {2024}, abstract = {This cumulative dissertation contains selected contributions to the field of asymptotic geometric analysis and high-dimensional probability. It is divided into two chapters: Chapter 1 explains some of the necessary theoretical background. In Section 1.1 it first gives a very concise history of asymptotic geometric analysis in general and then of the objects under study in particular, setting out some cornerstones in the discovery of the functional-analytic, geometric, and probabilistic properties of the spaces under consideration. The next section (1.2) gives the precise definitions and very basic properties of the three lp-type spaces that play a role in the contributed articles: the classical lp-sequence spaces, the mixed-norm sequence spaces, and the Schatten-classes Sp, each in its infinite- and finite-dimensional version. Section 1.3 is dedicated to the interplay between geometry and probability, expounding the general idea, introducing a few of the common tools, and exemplifying these on two kinds of limit theorems: Schechtman-Schmuckenschl{\"a}ger-type results and Poincar{\´e}-Maxwell-Borel lemmas. The first chapter concludes with Section 1.4, addressing a small sample of open questions pertaining to the contributed articles which are not answered in said articles and may be the interest of future research. The entirety of Chapter 2 consists of the contributed articles.}, language = {en} }