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3044 results in Probability theory and stochastic processes

Page 60 of 153

Convergence of One-Parameter Operator Semigroups
  • In Models of Mathematical Biology and Elsewhere
  • Adam Bobrowski
  • Published online:
    05 July 2016
    Print publication:
    14 July 2016
  • This book presents a detailed and contemporary account of the classical theory of convergence of semigroups and its more recent development treating the case where the limit semigroup, in contrast to the approximating semigroups, acts merely on a subspace of the original Banach space (this is the case, for example, with singular perturbations). The author demonstrates the far-reaching applications of this theory using real examples from various branches of pure and applied mathematics, with a particular emphasis on mathematical biology. The book may serve as a useful reference, containing a significant number of new results ranging from the analysis of fish populations to signaling pathways in living cells. It comprises many short chapters, which allows readers to pick and choose those topics most relevant to them, and it contains 160 end-of-chapter exercises so that readers can test their understanding of the material as they go along.

Random Graphs, Geometry and Asymptotic Structure
  • Michael Krivelevich, Konstantinos Panagiotou, Mathew Penrose, Colin McDiarmid
  • Edited by Nikolaos Fountoulakis, Dan Hefetz
  • Published online:
    05 May 2016
    Print publication:
    25 April 2016
  • The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.

  • Editors’ introduction

  • Michael Krivelevich, Tel-Aviv University, Konstantinos Panagiotou, Universität Munchen, Mathew Penrose, University of Bath, Colin McDiarmid, University of Oxford
  • Edited by Nikolaos Fountoulakis, University of Birmingham, Dan Hefetz, University of Birmingham
  • Book:
    Random Graphs, Geometry and Asymptotic Structure
    Published online:
    05 May 2016
    Print publication:
    25 April 2016, pp 1-3

  • Summary

    The theory of random graphs was established during the 1950s through the pioneering work of Gilbert and subsequently of Erdős and Rényi who set its foundations. Since then, the theory has been developed vastly and is by now a central area of combinatorics. Numerous, often unexpected, ramifications have emerged, which link it to diverse areas of mathematics such as number theory, combinatorial optimization and probability theory. Since its beginning, the study of geometric and topological aspects of random graphs has become the meeting point between combinatorics and areas of probability theory, such as percolation theory and stochastic processes. Nowadays, this interface has been consolidated through numerous deep results. This has led to applications in other scientific disciplines including telecommunications, astronomy, statistical physics, biology and computer science, as well as much more recent developments such as the study of social and biological networks.

    The present book is the outcome of a short course that took place at the School of Mathematics of the University of Birmingham in August 2013 and was supported by the London Mathematical Society and the Engineering and Physical Sciences Research Council. Its aim was to provide a concise overview of recent trends in the theory of random graphs, ranging from classical structural problems to geometric and topological aspects, and to introduce the participants to new powerful complex–analytic techniques and stochastic models that have led to recent breakthroughs in the field.

    The theory of random graphs is nowadays part and parcel of the education of any young researcher entering the fascinating world of combinatorics. However, due to their interdisciplinary nature, the geometric and structural aspects of the theory often remain an obscure part of the education of young researchers. Moreover, the theory itself, even in its most basic forms, is often considered quite advanced to be part of undergraduate curricula, and those interested, usually learn it mostly through self-study, covering a lot of its fundamentals but not much of the more recent developments. The present book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory of random graphs and introduces the reader to the diversity and depth of the methods that have been invented in this context.

Page 60 of 153