The third edition of this successful text gives a rigorous introduction to probability theory and the discussion of the most important random processes in some depth. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable to the beginner, and provides a taste and encouragement for more ...
This book is a revised, updated and greatly expanded version of the authors' "Probability and Random Processes: Problems and Solutions", first published in 1992. The 1000+ exercises contained within are not merely drill problems but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the student. ...
Polycrystalline metals, porous rocks, colloidal suspensions, epitaxial thin films, gels, foams, granular aggregates, sea ice, shape-memory metals, magnetic materials, and electro-rheological fluids are all examples of materials where an understanding of the mathematics on the different length scales is a key to interpreting their physical behavior ...
The random-cluster model has emerged in recent years 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. This systematic study includes accounts of the subcritical and supercritical phases, ...
Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty and difficulty. Percolation is pivotal for studying more complex physical systems exhibiting phase transitions. The emphasis of this book is upon core mathematical ...
Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation, and has taught, influenced and inspired generations of students and researchers in mathematics. This volume summarises and reviews the consistent themes from his work through a series ...
This volume contains lectures on probability theory and statistics. They examine decoupling and limit theorems for U-statistics and U-processes, aspects theory of the bootstrap, percolation and disordered systems, and finite Markov Chains.
This book contains around 675 problems in probability and random processes, together with their solutions. Apart from being a volume of worked problems in its own right, it is also a solutions manual for exercises and problems appearing in the companion volume, "Probability and Random Processes". Despite being intended in part as a companion, the ...
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