Advances in Disordered Systems, Random Processes and Some Applications

Contucci, Pierluigi (EDT)/ Giardinà, Cristian (EDT)

Cambridge University Press（2016/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 380 p.
• 言語 ENG
• 商品コード 9781107124103
• DDC分類 530

Full 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.

Contents

Preface; 1. Topological field theory of data: mining data beyond complex networks? Mario Rasetti and Emanuela Merelli; 2. A random walk in diffusion phenomena and statistical mechanics Elena Agliari; 3. Legendre structures in statistical mechanics for ordered and disordered systems Francesco Guerra; 4. Extrema of log-correlated random variables: principles and examples Louis-Pierre Arguin; 5. Scaling limits, Brownian loops and conformal fields Federico Camia; 6. The Brownian web, the Brownian net, and their universality Emmanuel Schertzer, Rongfeng Sun and Jan M. Swart; Index.