Multiplicative cascades are fractal random measures introduced by Mandelbrot to model turbulency phenomena. These measures are parametrized by a positive random variable W and an integer r, and defined on the boundary of the r-ary tree. In this talk, we will look at the limiting behaviour of the cascade as r goes to infinity, focusing on the large deviations. When the decay of the tail of W is super-exponential, the large deviations are explained by the deviations of the first level in the tree. This is not true anymore when the decay of the tail of W is only (sub-)exponential: in this case, the large deviations are obtained as the deviation of a finite-length spine in the tree.
