Critical Mandelbrot Cascades
Seminar Room 1, Newton Institute
AbstractMandelbrot'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.
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