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Critical Mandelbrot Cascades

Kupiainen, A (University of Helsinki)
Monday 17 September 2012, 16:10-16:50

Seminar Room 1, Newton Institute


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.


[pdf ]


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