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Statistical Mechanics of Classical and Disordered Systems
These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.
A First Course in Stochastic Calculus
A First Course in Stochastic Calculus is a complete guide for advanced undergraduate students to take the next step in exploring probability theory and for master's students in mathematical finance who would like to build an intuitive and theoretical understanding of stochastic processes. This book is also an essential tool for finance professionals who wish to sharpen their knowledge and intuition about stochastic calculus. Louis-Pierre Arguin offers an exceptionally clear introduction to Brownian motion and to random processes governed by the principles of stochastic calculus. The beauty and power of the subject are made accessible to readers with a basic knowledge of probability, linear a...
Perspectives on Spin Glasses
Presenting and developing the theory of spin glasses for mathematical physicists and probabilists working in disordered systems.
Topics in Applied Mathematics and Modeling
The analysis and interpretation of mathematical models is an essential part of the modern scientific process. Topics in Applied Mathematics and Modeling is designed for a one-semester course in this area aimed at a wide undergraduate audience in the mathematical sciences. The prerequisite for access is exposure to the central ideas of linear algebra and ordinary differential equations. The subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have ...
Stability of Queueing Networks
Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen.
Sojourns in Probability Theory and Statistical Physics - I
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. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.
Spin Glasses and Complexity
This primer builds the theory of spin glasses, starting with the real physical systems and experiments that inspired the theory.
A Bridge to Advanced Mathematics
Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn a...
Progress in High-Dimensional Percolation and Random Graphs
This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part...
An Introduction to Real Analysis
An Introduction to Real Analysis gives students of mathematics and related sciences an introduction to the foundations of calculus, and more generally, to the analytic way of thinking. The authors' style is a mix of formal and informal, with the intent of illustrating the practice of analysis and emphasizing the process as much as the outcome. The book is intended for use in a one- or two-term course for advanced undergraduates in mathematics and related fields who have completed two or three terms of a standard university calculus sequence.
