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Lectures on Probability Theory and Statistics

Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003

  • Editors
  • Jean Picard

Part of the Lecture Notes in Mathematics book series (LNM, volume 1869)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Amir Dembo, Tadahisa Funaki
    Pages 1-101
  3. Amir Dembo, Tadahisa Funaki
    Pages 103-274
  4. Back Matter
    Pages 275-281

About this book

Introduction

This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.

Keywords

Brownian motion Hydrodynamic limit Markov chain Multi-fractal analysis Probability theory Random interfaces random walk statistics

Bibliographic information

  • DOI https://doi.org/10.1007/b136622
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-26069-1
  • Online ISBN 978-3-540-31537-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site