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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.

Mathematical physics. --- Random matrices. --- Stochastic processes. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Functions. --- Analysis (Mathematics) --- Matrices, Random --- Mathematics. --- Functional analysis. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Functional Analysis. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Differential equations --- Mathematical analysis --- Numbers, Complex --- Set theory --- Calculus --- Matrices --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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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.

Mathematics --- Functional analysis --- Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- functies (wiskunde) --- wiskunde --- kansrekening

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Mathematics

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Als in der deutschen Spätaufklärung ›Anthropologie‹ und Ästhetik eine enge Allianz eingehen, stürzt dies eine alte Gattung in die Krise, die nun zum anti-anthropologischen Textmuster schlechthin avanciert: die ›literarische Utopie‹. Fiktionale Texte über Gesellschaften vernunftautonomer Individuen widersprechen jenem neuen Menschenbild, das die Macht körperlicher Konditionen über das Denken und Handeln betont. Gerade wegen ihres zweifelhaften Rufs bietet die ›literarische Utopie‹ aber zugleich Gelegenheit, die ›Anthropologie‹ als problematischen und politisch brisanten Wissensbestand zu reflektieren, hinter dem die Nihilismusgefahr wie ein Gespenst lauert. Untersucht wird daher, wie Autoren der selbstreflexiven Aufklärung und Frühromantik mit diesem Textmuster auf die ›Rehabilitation der Sinnlichkeit‹ und die dadurch verursachten ethischen, theologischen, politischen und ästhetischen Probleme reagieren. Literaturhistorisch diskutiert die Studie am Fall einer Gattung Kontinuitäten und Diskontinuitäten zwischen Spätaufklärung und Frühromantik, systematisch zielt sie auf eine Modellierung von Literatur- und Gattungsgeschichte als Problemgeschichte.

Utopias --- History. --- Anthropology. --- Enlightenment. --- Romanticism. --- Utopia.

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Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of  a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.

Mathematics --- Number theory --- Functional analysis --- Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- functies (wiskunde) --- wiskunde --- kansrekening --- getallenleer