Statistical Physics Landau Lifschitz

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck`s 70th birthday.

This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks.

This book bridges the gap between advances in the communities of computer science and physics–namely machine learning and statistical physics. It contains diverse but relevant topics in statistical physics, complex systems, network theory, and machine learning. Examples of such topics are: predicting missing links, higher-order generative modeling of networks, inferring network structure by tracking the evolution and dynamics of digital traces, recommender systems, and diffusion processes.

During the recent years the interest in limit theorems for dependent random variables has considerably grown being stimulated both by requirements of probability theory and by many applied disciplines. A special place among such disciplines belongs to statistical physics whose mathematical apparatus for a long time has been developing regardless the probability theory. However recently a process of mutual understanding between the specialists of this two fields started to develop. This resulted in a burst of activity for the benefit of both the subjects. For instance, the concept of Gibbs random field which has originated in statistical physics became a powerful stimulus for development of the theory of random fields while the Gibbsian fields themselves turned out to be excellent object for application of many general probabilistic results.

Thermal processes are ubiquitous and an understanding of thermal phenomena is essential for a complete description of the physics of nanoparticles, both for the purpose of modeling the dynamics of the particles and for the correct interpretation of experimental data.

The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently.

This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks.

The book is divided into two parts. The first part looks at the modeling of statistical systems before moving on to an analysis of these systems.