Part of Cambridge Series in Statistical and Probabilistic Mathematics
Publication planned for: December 2016
availability: Not yet published - available from December 2016
format: Hardback
isbn: 9781107160156
Starting around the late 1950s, several research communities started relating the geometry of graphs to the stochastic processes on these graphs. This book, 20 years in the making, ties together the research in the field, bringing together work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 800 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.
Provides broad and deep coverage of most key aspects of probability on graphs and their interconnections, including the best proofs available of many important results
Detailed end-chapter notes give context and further reading
More than 850 exercises allow readers to develop their skills and apply the key techniques
1. Some highlights
2. Random walks and electric networks
3. Special networks
4. Uniform spanning trees
5. Branching processes, second moments, and percolation
6. Isoperimetric inequalities
7. Percolation on transitive graphs
8. The mass-transport technique and percolation
9. Infinite electrical networks and Dirichlet functions
10. Uniform spanning forests
11. Minimal spanning forests
12. Limit theorems for Galton?Watson processes
13. Escape rate of random walks and embeddings
14. Random walks on groups and Poisson boundaries
15. Hausdorff dimension
16. Capacity
17. Random walks on Galton-Watson trees.
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: January 2017
availability: Not yet published - available from January 2017
format: Hardback
isbn: 9781107140516
Thanks to the driving forces of the Ito calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.
Develops the It o and the Malliavin calculi in tandem
Details foundations and applications of Stochastic calculus
Provides a path space analysis point of view
Preface
Frequently used notation
1. Fundamentals of continuous stochastic processes
2. Stochastic integrals and Ito's formula
3. Brownian motion and Laplacian
4. Stochastic differential equations
5. Malliavin calculus
6. Black-Scholes model
7. Semiclassical limit
Appendix
References
Subject index.
The core of this monograph is the development of tools to derive well-posedness
results in very general geometric settings for elliptic differential operators. A
new generation of Calderon-Zygmund theory is developed for variable
coefficient singular integral operators. At the intersection of PDEs, harmonic
analysis and differential geometry this text is suitable for a wide range of PhD
students, researchers and professionals.
D. Mitrea and M. Mitrea, Univ. of Missouri, USA;
I. Mitrea, Temple Univ., Philadelphia, USA;
M. Taylor, Univ. of North Carolina, USA.
De Gruyter Studies in Mathematics 64
xii, 580 pages
Hardcover:
ISBN 978-3-11-048266-9
Date of Publication: September 2016
Language of Publication: English
Subjects:
Differential Equations and Dynamical Systems
Geometry and Topology
October 15, 2016 Forthcoming
Textbook - 450 Pages - 50 B/W Illustrations
ISBN 9781498777605 - CAT# K29775
Series: Discrete Mathematics and Its Applications
Covers key families of functions, including Catalan, Bell, and Stirling numbers
Gives many examples, more than competing books
Offers unique, modern applications to student life
Uses Mathematica and Maple
The purpose of this undergraduate textbook is to offer all the material suitable for a beginning combinatorics course for students in STEM subjects particularly mathematics and computer science, although other subjects may benefit as well. This will be achieved through the use of plentiful (though brief) examples, and a variety of exercises and problems. In addition, we use in our examples more up-to-date ideas (such as digital music files rather than books on a shelf) and give some code to assist the student with the use of Mathematica, Maple, and other technological tools.
Instructors
We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption.
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Introduction. Fundamentals of Enumeration. Fundamentals of Probability. The Pigeonhole Principle and Ramsey's Theorem. The Principle of Inclusion and Exclusion. Generating Functions and Recurrence Relations. Catalan, Bell and Stirling Numbers. Symmetries and the Polya-Redfield Method. Posets. Introduction to Graph Theory. Further Graph Theory. Coding Theory. Latin Squares. Balanced Incomplete Block Designs. Linear Algebra Methods in Combinatorics. Appendices.