Gerold Alsmeyer & Matthias Löwe 
Random Matrices and Iterated Random Functions [PDF ebook] 
Münster, October 2011

​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.

Table of Content

​​ ​E. Le Page: Tails of a stationary probability measure for an affine stochastic recursion on the line.- Yv. Guivarc’h: On homogeneity at infinity of stationary measures for affine stochastic recursions.- M. Stolz: Limit theorems for random elements of the compact classical groups.- T. Kriecherbauer: Universality of local eigenvalue statistics.- R. Speicher: Asymptotic eigenvalue distribution of random matrices and free stochastic analysis.- M. Peigné: Conditioned random walk in Weyl chambers and renewal theory in a cone.- D. Buraczewski: The linear stochastic equation R =_d /sum_{ i=1}^N A_i R_i + B in the critical case.- J. Collamore: Tail estimates for stochastic fixed point equations.- S. Mentemeier: On multivariate random difference equations.- M. Olvera-Cravioto: Tail asymptotics for solutions of stochastic fixed point equations on trees.- E. Damek: On fixed points of generalized multidimensional affine recursions.- G. Alsmeyer: The functional equation of the smoothing transform.– O. Friesen, M. Löwe: Limit theorems for the eigenvalues of random matrices with weakly correlated entries.