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Critical Mandelbrot Cascades

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Mathematics and Physics of Anderson localization: 50 Years After

Mandelbrot’s multiplicative cascade measures are random energy models with logarithmically correlated energies. They exhibit a freezing transition from high temperature phase with (singular) continuous Gibbs measure to an atomic one in low temperatures. I will discuss recent work proving that in the critical case these measures have no atoms. I also discuss the multi fractal spectrum and the KPZ formula of Liouville gravity at the critical point and low temperature phase.

This talk is part of the Isaac Newton Institute Seminar Series series.

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