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- W2740536030 abstract "Some of the most interesting and challenging problems in theoretical and mathematical physics have been the ones involving in an essential way several distance scales. Such problems include the theory of critical phenomena and phase transitions, the problem of the existence of relativistic quantum field theories, the turbulent behaviour in hydrodynamic systems and many others. While many of these problems date back several decades (or, indeed, to the previous century), significant progress was made only in the 60s, mainly in the context of critical phenomena, using ideas stressing the role of scale invariance in such problems. This line of thought culminated with the creation of the theory of the Renormalization Group (RG) by K.Wilson (see [1] for the history) that provided a unified method of attack for multiscale problems. The 70s saw the RG-theory vindicated in approximative analytic treatments of a multitude of problems in critical phenomena, hydrodynamics and other many-body systems. With the increasing power of computers, the ideas entered numerical analysis of such problems in the 80s. On the mathematical side, RG ideas lead to the rigorous theory of so-called renormalizable quantum field theories (and a non-renormalizable one too) and some critical statistical mechanics problems [2] (these works by no means exhaust the mathematical progress in these fields, nor even the RG inspired works, for a rather recent set of references, see [3]. In this talk I would like to review some recent attempts to develope a mathematical RG theory for the study of so-called random (or disordered) systems. Again, this field has seen plenty of beautiful mathematical work, some of it RG inspired too, but no attempt is being made here for a comprehensive review." @default.
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- W2740536030 title "Renormalization Group and Random Systems" @default.
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