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9781107458437

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'An understanding of the remarkable properties of the Poisson process is essential for anyone interested in the mathematical theory of probability or in its many fields of application. This book is a lucid and thorough account, rigorous but not pedantic, and accessible to any reader familiar with modern mathematics at first degree level. Its publication is most welcome.' J. F. C. Kingman, University of Bristol 'I have always considered the Poisson process to be a cornerstone of applied probability. This excellent book demonstrates that it is a whole world in and of itself. The text is exciting and indispensable to anyone who works in this field.' Dietrich Stoyan, Technische Universitat Bergakademie Freiberg , Germany 'Last and Penrose's Lectures on the Poisson Process constitutes a splendid addition to the monograph literature on point processes. While emphasizing the Poisson and related processes, their mathematical approach also covers the basic theory of random measures and various applications, especially to stochastic geometry. They assume a sound grounding in measure-theoretic probability, which is well summarized in two appendices (on measure and probability theory). Abundant exercises conclude each of the twenty-two 'lectures' which include examples illustrating their 'course' material. It is a first-class complement to John Kingman's essay on the Poisson process.' Daryl Daley, University of Melbourne 'Pick n points uniformly and independently in a cube of volume n in Euclidean space. The limit of these random configurations as n â â is the Poisson process. This book, written by two of the foremost experts on point processes, gives a masterful overview of the Poisson process and some of its relatives. Classical tenets of the Theory, like thinning properties and Campbell's formula, are followed by modern developments, such as Liggett's extra heads theorem, Fock space, permanental processes and the Boolean model. Numerous exercises throughout the book challenge readers and bring them to the edge of current theory.' Yuval Peres, Microsoft Research and National Academy of Sciences

Advance praise: 'An understanding of the remarkable properties of the Poisson process is essential for anyone interested in the mathematical theory of probability or in its many fields of application. This book is a lucid and thorough account, rigorous but not pedantic, and accessible to any reader familiar with modern mathematics at first degree level. Its publication is most welcome.' J. F. C. Kingman, University of Bristol Advance praise: 'I have always considered the Poisson process to be a cornerstone of applied probability. This excellent book demonstrates that it is a whole world in and of itself. The text is exciting and indispensable to anyone who works in this field.' Dietrich Stoyan, Technische Universitat Bergakademie Freiberg , Germany Advance praise: 'Last and Penrose's Lectures on the Poisson Process constitutes a splendid addition to the monograph literature on point processes. While emphasizing the Poisson and related processes, their mathematical approach also covers the basic theory of random measures and various applications, especially to stochastic geometry. They assume a sound grounding in measure-theoretic probability, which is well summarized in two appendices (on measure and probability theory). Abundant exercises conclude each of the twenty-two 'lectures' which include examples illustrating their 'course' material. It is a first-class complement to John Kingman's essay on the Poisson process.' Daryl Daley, University of Melbourne Advance praise: 'Pick n points uniformly and independently in a cube of volume n in Euclidean space. The limit of these random configurations as n â â is the Poisson process. This book, written by two of the foremost experts on point processes, gives a masterful overview of the Poisson process and some of its relatives. Classical tenets of the Theory, like thinning properties and Campbell's formula, are followed by modern developments, such as Liggett's extra heads theorem, Fock space, permanental processes and the Boolean model. Numerous exercises throughout the book challenge readers and bring them to the edge of current theory.' Yuval Peres, Microsoft Research and National Academy of Sciences

'An understanding of the remarkable properties of the Poisson process is essential for anyone interested in the mathematical theory of probability or in its many fields of application. This book is a lucid and thorough account, rigorous but not pedantic, and accessible to any reader familiar with modern mathematics at first degree level. Its publication is most welcome.' J. F. C. Kingman, University of Bristol 'I have always considered the Poisson process to be a cornerstone of applied probability. This excellent book demonstrates that it is a whole world in and of itself. The text is exciting and indispensable to anyone who works in this field.' Dietrich Stoyan, Technische Universitat Bergakademie Freiberg , Germany 'Last and Penrose's Lectures on the Poisson Process constitutes a splendid addition to the monograph literature on point processes. While emphasizing the Poisson and related processes, their mathematical approach also covers the basic theory of random measures and various applications, especially to stochastic geometry. They assume a sound grounding in measure-theoretic probability, which is well summarized in two appendices (on measure and probability theory). Abundant exercises conclude each of the twenty-two 'lectures' which include examples illustrating their 'course' material. It is a first-class complement to John Kingman's essay on the Poisson process.' Daryl Daley, University of Melbourne 'Pick n points uniformly and independently in a cube of volume n in Euclidean space. The limit of these random configurations as n is the Poisson process. This book, written by two of the foremost experts on point processes, gives a masterful overview of the Poisson process and some of its relatives. Classical tenets of the Theory, like thinning properties and Campbell's formula, are followed by modern developments, such as Liggett's extra heads theorem, Fock space, permanental processes and the Boolean model. Numerous exercises throughout the book challenge readers and bring them to the edge of current theory.' Yuval Peres, Microsoft Research and National Academy of Sciences 'An understanding of the remarkable properties of the Poisson process is essential for anyone interested in the mathematical theory of probability or in its many fields of application. This book is a lucid and thorough account, rigorous but not pedantic, and accessible to any reader familiar with modern mathematics at first degree level. Its publication is most welcome.' J. F. C. Kingman, University of Bristol 'I have always considered the Poisson process to be a cornerstone of applied probability. This excellent book demonstrates that it is a whole world in and of itself. The text is exciting and indispensable to anyone who works in this field.' Dietrich Stoyan, Technische Universitat Bergakademie Freiberg , Germany 'Last and Penrose's Lectures on the Poisson Process constitutes a splendid addition to the monograph literature on point processes. While emphasizing the Poisson and related processes, their mathematical approach also covers the basic theory of random measures and various applications, especially to stochastic geometry. They assume a sound grounding in measure-theoretic probability, which is well summarized in two appendices (on measure and probability theory). Abundant exercises conclude each of the twenty-two `lectures' which include examples illustrating their `course' material. It is a first-class complement to John Kingman's essay on the Poisson process.' Daryl Daley, University of Melbourne 'Pick n points uniformly and independently in a cube of volume n in Euclidean space. The limit of these random configurations as n is the Poisson process. This book, written by two of the foremost experts on point processes, gives a masterful overview of the Poisson process and some of its relatives. Classical tenets of the Theory, like thinning properties and Campbell's formula, are followed by modern developments, such as Liggett's extra heads theorem, Fock space, permanental processes and the Boolean model. Numerous exercises throughout the book challenge readers and bring them to the edge of current theory.' Yuval Peres, Microsoft Research and National Academy of Sciences

Author Information

Günter Last is Professor of Stochastics at the Karlsruhe Institute of Technology, Germany. He is a distinguished probabilist with particular expertise in stochastic geometry, point processes, and random measures. He coauthored a research monograph on marked point processes on the line as well as two textbooks on general mathematics. He has given many invited talks on his research worldwide. Mathew Penrose is Professor of Probability at the University of Bath. He is an internationally leading researcher in stochastic geometry and applied probability and is the author of the influential monograph Random Geometric Graphs (2003). He received the Friedrich Wilhelm Bessel Research Award from the Humboldt Foundation in 2008, and has held visiting positions as guest lecturer in New Delhi, Karlsruhe, San Diego, Birmingham, and Lille.

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