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Stochastic Analysis in Mathematical Physics
The ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang-Mills theory and spin-glass theory.The proper concept of stochastic dynamics relevant to each type of application is described in detail here. Altogether, these approaches illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come.
Stochastic Analysis
This book deals with current developments in stochastic analysis and its interfaces with partial differential equations, dynamical systems, mathematical physics, differential geometry, and infinite-dimensional analysis. The origins of stochastic analysis can be found in Norbert Wiener's construction of Brownian motion and Kiyosi Itô's subsequent development of stochastic integration and the closely related theory of stochastic (ordinary) differential equations. The papers in this volume indicate the great strides that have been made in recent years, exhibiting the tremendous power and diversity of stochastic analysis while giving a clear indication of the unsolved problems and possible future directions for development. The collection represents the proceedings of the AMS Summer Institute on Stochastic Analysis, held in July 1993 at Cornell University. Many of the papers are largely expository in character while containing new results.
Stochastic Analysis In Mathematical Physics - Proceedings Of A Satellite Conference Of Icm 2006
The ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang-Mills theory and spin-glass theory.The proper concept of stochastic dynamics relevant to each type of application is described in detail here. Altogether, these approaches illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come./a
Mathematical Systems Theory in Biology, Communications, Computation and Finance
This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.
An Intuitive Exploration of Artificial Intelligence
This book develops a conceptual understanding of Artificial Intelligence (AI), Deep Learning and Machine Learning in the truest sense of the word. It is an earnest endeavor to unravel what is happening at the algorithmic level, to grasp how applications are being built and to show the long adventurous road in the future. An Intuitive Exploration of Artificial Intelligence offers insightful details on how AI works and solves problems in computer vision, natural language understanding, speech understanding, reinforcement learning and synthesis of new content. From the classic problem of recognizing cats and dogs, to building autonomous vehicles, to translating text into another language, to au...
Xivth International Congress On Mathematical Physics
In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in math...
Spin Glasses and Complexity
This primer builds the theory of spin glasses, starting with the real physical systems and experiments that inspired the theory.
Finance at Fields
This outstanding collection of articles includes papers presented at the Fields Institute, Toronto, as part of the Thematic Program in Quantitative Finance that took place in the first six months of the year 2010. The scope of the volume is very broad, with papers on foundational issues in mathematical finance, papers on computational finance, and papers on derivatives and risk management. Many of the articles contain path-breaking insights that are relevant to the developing new order of post-crisis financial risk management.
Probability and Analysis in Interacting Physical Systems
This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15–19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics.
Lattice Models and Conformal Field Theory
This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a well-posed road from simple lattice models to CFTs. Structured in two parts, the book begins by exploring several two-dimensional lattice models, their phase transitions, and their conjectural connection with CFT. Through these lattice models and their local fields, the fundamental ideas and results of two-dimensional CFTs emerge, with a special emphasis on the Unitary Minimal Models of CFT. Delving into the delicate ideas that lead to the classification of these CFTs, the authors discuss the assumpti...
