Gaussian Processes on Trees

This book offers a clear introduction to branching Brownian motion, exploring its connections to extreme value theory and statistical physics, while detailing recent advancements for graduate students and researchers in the field.

Gaussian Processes on Trees serves as a comprehensive introduction to the intricate world of branching Brownian motion (BBM), a significant model that intersects value statistics for Gaussian processes, statistical physics, and non-linear partial differential equations. Aimed at graduate students and researchers, the book provides a clear pathway to understanding the latest advancements in this dynamic field of study. The author emphasizes the foundational role of BBM in probability theory and its profound links to partial differential equations.

The text begins with a succinct overview of classical extreme value statistics and an introductory discussion on mean-field spin glasses, setting the stage for a deeper exploration of BBM. The author meticulously reviews the classical findings of Bramson regarding the asymptotic behavior of solutions to the F-KPP equation. This foundational knowledge is then applied to the recent developments in the extremal process of BBM, illustrating the relevance of these concepts in contemporary research.

Furthermore, the book delves into the extension of established results to cases of branching Brownian motion with variable speed, enriching the reader's understanding of the subject. Designed to be self-contained, it caters to graduate students with a foundational knowledge of probability theory, making it an excellent resource for those eager to delve into the fascinating interplay between mathematics, statistical mechanics, and extreme value theory. Overall, Gaussian Processes on Trees is a valuable contribution to the literature, inviting readers to engage with the complexities of this vibrant area of research.