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High Dimensional Probability

  • Ernst Eberlein
  • Marjorie Hahn
  • Michel Talagrand

Part of the Progress in Probability book series (PRPR, volume 43)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Amir Dembo, Qi-Man Shao
    Pages 27-32
  3. T. Dunker, M. A. Lifshits, W. Linde
    Pages 59-74
  4. Uwe Einmahl, David M. Mason
    Pages 75-92
  5. Peter Gaenssler, Daniel Rost, Klaus Ziegler
    Pages 93-102
  6. Bernhard Heinkel
    Pages 145-149
  7. Jørgen Hoffmann-Jørgensen
    Pages 151-189
  8. Wenbo V. Li, James Kuelbs
    Pages 233-243
  9. Wenbo V. Li, Geoffrey Pritchard
    Pages 245-248
  10. Mikhail Lifshits, Michel Weber
    Pages 249-261
  11. Back Matter
    Pages 332-335

About these proceedings

Introduction

What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.

Keywords

Estimator Gaussian measure Probability Random variable Stochastic processes mixing random measure statistics stochastic process

Editors and affiliations

  • Ernst Eberlein
    • 1
  • Marjorie Hahn
    • 2
  • Michel Talagrand
    • 3
  1. 1.Institut für Mathematische StochastikUniversität FreiburgFreiburgGermany
  2. 2.Department of MathematicsTufts UniversityMedfordUSA
  3. 3.Equipe d’analyse, Tour 46Université Paris VIParis Cedex 05France

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