Random Matrices and Iterated Random Functions

1. Front Matter

   Pages i-viii

   PDF

2. Random Matrices

   1. Front Matter

      Pages 1-1

      PDF

   2. On the Limiting Spectral Density of Symmetric Random Matrices with Correlated Entries

      • Olga Friesen, Matthias Löwe

      Pages 3-29

   3. Asymptotic Eigenvalue Distribution of Random Matrices and Free Stochastic Analysis

      • Roland Speicher

      Pages 31-44

   4. Spacings: An Example for Universality in Random Matrix Theory

      • Thomas Kriecherbauer, Kristina Schubert

      Pages 45-71

   5. Stein’s Method and Central Limit Theorems for Haar Distributed Orthogonal Matrices: Some Recent Developments

      • Michael Stolz

      Pages 73-88

3. Iterated Random Functions

   1. Front Matter

      Pages 89-89

      PDF

   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

​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.

• 60B20, 46L54, 60B15, 60F05, 60J05, 60J80, 60K05
• free probability
• implicit renewal theory
• iterated random functions
• random matrices/difference equations
• stochastic fixed point equations

• 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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