abstract
The goal is to understand sample-to-sample fluctuations in disorder-generated multifractal intensity patterns. Arguably the simplest model of that sort is the exponential of an ideal periodic 1/f Gaussian noise. The latter process can be looked at as a one-dimensional “projection” of 2D Gaussian Free Field and inherits from it the logarithmic covariance structure. It most naturally emerges in the random matrix theory context, but attracted also an independent interest in statistical mechanics of disordered systems. I will determine the threshold of extreme values of 1/f noise and provide a rather compelling explanation for the mechanism behind its universality. Revealed mechanisms are conjectured to retain their qualitative validity for a broad class of disorder-generated multifractal fields.
The presentation will be mainly based on the joint work with Pierre Le Doussal and Alberto Rosso, J Stat Phys: 149 (2012), 898-920 as well as on some related earlier works by the speaker.