Asymptotic Geometric Analysis, Part I
This book by Shiri Artstein-Avidan, Apostolos Giannopoulos, and Vitali D. Milman develops the theory of asymptotic geometric analysis, a field on the border between geometry and functional analysis. Isometric problems typical of low-dimensional geometry are replaced by an isomorphic point of view, and an asymptotic approach as the dimension tends to infinity is introduced. A central theme is the interaction of randomness and pattern, including the concentration of measure phenomenon and isoperimetric inequalities in isomorphic form.