Advances in Disordered Systems, Random Processes and Some Applications

Description

This book offers a unified perspective on the study of complex systems for scholars of various disciplines, including mathematics, physics, computer science, biology, economics and social science. The contributions, written by leading scientists, cover a broad set of topics, including new approaches to data science, the connection between scaling limits and conformal field theories, and new ideas on the Legendre duality approach in statistical mechanics of disordered systems. The volume moreover explores results on extreme values of correlated random variables and their connection with the Riemann zeta functions, the relation between diffusion phenomena and complex systems, and the Brownian web, which appears as the universal scaling limit of several probabilistic models. Written for researchers from a broad range of scientific fields, this text examines a selection of recent developments in complex systems from a rigorous perspective. List of Contributors......Page 6 Preface......Page 9 1 Topological Field Theory of Data: Mining Data Beyond Complex Networks......Page 12 2 A Random Walk in Diffusion Phenomena and Statistical Mechanics......Page 54 3 Legendre Structures in Statistical Mechanics for Ordered and Disordered Systems......Page 153 4 Extrema of Log-correlated Random Variables: Principles and Examples......Page 177 5 Scaling Limits, Brownian Loops, and Conformal Fields......Page 216 6 The Brownian Web, the Brownian Net, and their Universality......Page 281 Index......Page 380