@MISC{Speicher_physicalapplications, author = {Roland Speicher}, title = {Physical Applications of Freeness}, year = {} }

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Abstract

Introduction The mathematical concept `freeness' was introduced by Voiculescu about 15 years ago in order to get some insight into the structure of the von Neumann algebras of the free groups. The starting idea of Voiculescu was to separate the notion of freeness from that concrete problem and to consider it on its own sake. One leading principle of his investigations was to consider freeness as a non-commutative analogue to the classical notion `independence of random variables' This approach was very successful. Gradually it became clear that freeness has indeed a very interesting structure of its own and that there exist a lot of links to other fields. One of the main links of freeness to an apriori unrelated context is the description of random matrices via freeness. This has opened the possibility to use freeness as an exact mathematical concept for the description of physical models and approximations which build (explicitely or implicitly) on random matrices. One model of