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Probability Theory

An Introductory Course

  • Yakov G. Sinai

Part of the Springer Textbook book series (SPRINGER TEXTB)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Yakov G. Sinai
    Pages 1-14
  3. Yakov G. Sinai
    Pages 43-53
  4. Yakov G. Sinai
    Pages 54-66
  5. Yakov G. Sinai
    Pages 67-72
  6. Yakov G. Sinai
    Pages 73-77
  7. Yakov G. Sinai
    Pages 78-82
  8. Yakov G. Sinai
    Pages 83-88
  9. Yakov G. Sinai
    Pages 89-94
  10. Yakov G. Sinai
    Pages 120-126
  11. Yakov G. Sinai
    Pages 134-138
  12. Back Matter
    Pages 139-140

About this book

Introduction

Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners. The first part of the book covers discrete random variables, using the same approach, basedon Kolmogorov's axioms for probability, used later for the general case. The text is divided into sixteen lectures, each covering a major topic. The introductory notions and classical results are included, of course: random variables, the central limit theorem, the law of large numbers, conditional probability, random walks, etc. Sinai's style is accessible and clear, with interesting examples to accompany new ideas. Besides statistical mechanics, other interesting, less common topics found in the book are: percolation, the concept of stability in the central limit theorem and the study of probability of large deviations. Little more than a standard undergraduate course in analysis is assumed of the reader. Notions from measure theory and Lebesgue integration are introduced in the second half of the text. The book is suitable for second or third year students in mathematics, physics or other natural sciences. It could also be usedby more advanced readers who want to learn the mathematics of probability theory and some of its applications in statistical physics.

Keywords

Probability theory Random variable Wahrscheinlichkeit Wahrscheinlichkeitstheorie conditional probability measure theory random walk

Authors and affiliations

  • Yakov G. Sinai
    • 1
  1. 1.L. D. Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02845-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-53348-1
  • Online ISBN 978-3-662-02845-2
  • Series Print ISSN 1431-8512
  • Buy this book on publisher's site