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Random Matrices and Iterated Random Functions

Münster, October 2011

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Gerold Alsmeyer

    1. Westphalian Wilhelms University Münster Institute of Mathematics and Informatics, Münster, Germany

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  2. Matthias Löwe

    1. Westphalian Wilhelms University Münster Institute for Mathematical Statistics, Münster, Germany

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    You can also search for this editor in PubMed   Google Scholar

  • Brings together two active areas of modern probability theory
  • Provides survey articles that are also readable for non-experts
  • Refereed according to journal standards
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 53)

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Table of contents (11 papers)

  1. Front Matter

    Pages i-viii
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  3. Iterated Random Functions

    1. Front Matter

      Pages 89-89
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    2. Large Deviation Tail Estimates and Related Limit Laws for Stochastic Fixed Point Equations

      • Jeffrey F. Collamore, Anand N. Vidyashankar
      Pages 91-117

    3. Homogeneity at Infinity of Stationary Solutions of Multivariate Affine Stochastic Recursions

      • Yves Guivarc’h, Émile Le Page
      Pages 119-135

    4. On Solutions of the Affine Recursion and the Smoothing Transform in the Critical Case

      • Sara Brofferio, Dariusz Buraczewski, Ewa Damek
      Pages 137-157

    5. Power Laws on Weighted Branching Trees

      • Predrag R. Jelenković, Mariana Olvera-Cravioto
      Pages 159-187

    6. The Smoothing Transform: A Review of Contraction Results

      • Gerold Alsmeyer
      Pages 189-228

    7. Precise Tail Index of Fixed Points of the Two-Sided Smoothing Transform

      • Gerold Alsmeyer, Ewa Damek, Sebastian Mentemeier
      Pages 229-251

    8. Conditioned Random Walk in Weyl Chambers and Renewal Theory

      • C. Lecouvey, E. Lesigne, M. Peigné
      Pages 253-265
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Keywords

About this book

​Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probability, non-commutative geometry, and dynamical systems. A great deal of recent work has focused on the study of spectra of large random matrices on the one hand and on iterated random functions, especially random difference equations, on the other. However, the methods applied in these two research areas are fairly dissimilar. Motivated by the idea that tools from one area could potentially also be helpful in the other, the volume editors have selected contributions that present results and methods from random matrix theory as well as from the theory of iterated random functions. This work resulted from a workshop that was held in Münster, Germany in 2011. The aim of the workshop was to bring together researchers from two fields of probability theory: random matrix theory and the theory of iterated random functions. Random matrices play fundamental, yet very different roles in the two fields. Accordingly, leading figures and young researchers gave talks on their field of interest that were also accessible to a broad audience.

Editors and Affiliations

  • Westphalian Wilhelms University Münster Institute of Mathematics and Informatics, Münster, Germany

    Gerold Alsmeyer

  • Westphalian Wilhelms University Münster Institute for Mathematical Statistics, Münster, Germany

    Matthias Löwe

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