To go further
Den Hollander, F. (2008). Large deviations (Vol. 14). American Mathematical Soc..
Kotz, S., & Nadarajah, S. (2000). Extreme value distributions: theory and applications. World Scientific.
Schmitt, F., Schertzer, D., Lovejoy, S., & Brunet, Y. (1994). Empirical study of multifractal phase transitions in atmospheric turbulence. Nonlinear Processes in Geophysics, 1(2/3), 95-104.
Schertzer, D., & Lovejoy, S. (1996). The multifractal phase transition route to self-organized criticality in turbulence and other dissipative nonlinear systems. Phys. Rep.
Lovejoy, S., & Schertzer, D. (2013). The weather and climate: emergent laws and multifractal cascades. Cambridge University Press.