Critical Gaussian Multiplicative Chaos: Convergence of the Derivative

Stochastic Analysis Seminar Series


Gaussian multiplicative chaos is a theory introduced by Kahane in 1985:this theory gives a rigorous mathematical meaning to measures whose density with respect to a reference measure is given by the  exponential of a Gaussian random variable living in the space of distributions (in the sense of Schwartz). This theory has many applications in a broad range of fields: finance, Liouville quantum gravity, turbulence, etc...In this talk, we will study Gaussian multiplicative chaos in the critical case (where Kahane's theory becomes trivial). We will show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to an atomless random measure with full support. Joint work with B. Duplantier, R. Rhodes and S. Sheffield.


Vincent Vargas (Université Paris-Dauphine)

Monday, February 4, 2013 - 15:45
to 16:45