Advances in Disordered Systems, Random Processes and Some Applications

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.

• Includes accounts of recent probabilistic methods used to investigate scaling limits from discrete to continuum models
• Maths and physics are presented side by side in order to solve current open problems in disordered systems
• Readers will be exposed to an up-to-date treatment of large databases, as well as to their theoretical modelisation