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Gibbs Measures and Phase Transitions
"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
Stochastics
This textbook, now in its second revised and extended edition, presents the fundamental ideas and results of both probability theory and statistics. It comprises the material of a one-year course, which is addressed to students of mathematics and to scientists with an interest in the mathematical side of stochastics. The stochastic concepts, models and methods are motivated by examples and then developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems, now in part with solutions, offer applications and supplements to the text.
Stochastics
This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.
Statistical Physics and Spatial Statistics
Modern physics is confronted with a large variety of complex spatial patterns. Although both spatial statisticians and statistical physicists study random geometrical structures, there has been only little interaction between the two up to now because of different traditions and languages. This volume aims to change this situation by presenting in a clear way fundamental concepts of spatial statistics which are of great potential value for condensed matter physics and materials sciences in general, and for porous media, percolation and Gibbs processes in particular. Geometric aspects, in particular ideas of stochastic and integral geometry, play a central role throughout. With nonspecialist researchers and graduate students also in mind, prominent physicists give an excellent introduction here to modern ideas of statistical physics pertinent to this exciting field of research.
A Modern Introduction to Probability and Statistics
Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books
Continuum Percolation
Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.
The Random-Cluster Model
The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Obsessed by a Dream
This Open Access biography chronicles the life and achievements of the Norwegian engineer and physicist Rolf Widerøe. Readers who meet him in the pages of this book will wonder why he isn't better known. The first of Widerøe's many pioneering contributions in the field of accelerator physics was the betatron. He later went on to build the first radiation therapy machine, an advance that would eventually revolutionize cancer treatment. Hospitals worldwide installed his machine, and today's modern radiation treatment equipment is based on his inventions. Widerøe's story also includes a fair share of drama, particularly during World War II when both Germans and the Allies vied for his collab...
The Reformation of Historical Thought
In The Reformation of Historical Thought, Mark Lotito re-examines the development of Western historiography by concentrating on Philipp Melanchthon (1497–1560) and his universal history, Carion’s Chronicle (1532). With the Chronicle, Melanchthon overturned the medieval papal view of history, and he offered a distinctly Wittenberg perspective on the foundations of the “modern” European world. Through its immense popularity, the Chronicle assumed extraordinary significance across the divides of language, geography and confession. Indeed, Melanchthon’s intervention would become the point of departure for theologians, historians and jurists to debate the past, present and future of the Holy Roman Empire. Through the Chronicle, the Wittenberg reformation of historical thought became an integral aspect of European intellectual culture for the centuries that followed.
