Probabilistic Symmetries and Invariance Principles

Focusing on the three fundamental symmetries of probability theory—contractability, exchangeability, and rotatability—this book presents a thorough exploration of their invariance properties. Building on de Finetti's foundational work, it delves into one and several dimensions, revealing surprising connections among the symmetries and their relevance to modern probability. Accessible to graduate students and researchers, the text includes comprehensive explanations and references, making it valuable for both probability and statistics scholars, as well as mathematicians in other disciplines.