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.

Pierluigi Contucci is Full Professor of Mathematical Physics at the University of Bologna. His research interests are mathematical physics and statistical mechanics and its applications. He is a member of the Istituto Cattaneo, Bologna, and in 2000 received the Schloessman Award from the Max Planck Society. Cristian Giardin... is Professor of Mathematical Physics at the University of Modena and Reggio Emilia, and currently also Visiting Full Professor of Probability at Delft University. His research interests are mathematical statistical physics and probability theory.