Gaussian Multiplicative Chaos – CHAMU

The project is centered on the study of Gaussian Multiplicative Chaos. This theory, initiated by J.P. Kahane in 1985, has recently found numerous applications in fundamental mathematics (Quantum gravity in dimension 2, conformal invariance), in the physics of Turbulence and Finance. This project, at the interface between mathematics and physics, is mainly concerned with reinforcing the applications in quantum gravity and turbulence. The members of the project are three mathematicians in the field of probability working at the CEREMADE (R. Allez, R. Rhodes et V. Vargas) and a physicist of turbulence working at the ENS Lyon (Laurent Chevillard).

More specifically, the members of the project will work on the following 3 points:

-KPZ (Quantum gravity in 2 dimensions): Establish a strong form of the KPZ equation relying the Euclidean dimensions to the Quantum dimensions.

-Matrix valued Chaos: Establish a matrix valued theory of Gaussian Multiplicative Chaos in the isotropic and non-isotropic case

-Turbulence (Modelling the velocity fied): based on the previous theory of matrix valued Gaussian Multiplicative Chaos, construct isotropic and incompressible random fields which satisfy the main properties observed on the velocity field in isotropic turbulence

The members of the project have already published articles on the 3 aforementionned points, by exploiting their scientific complementarity. Nevertheless, the members of the project want to reinforce their collaboration among themselves and with emeritus professors of the field. Therefore, they ask for funding for travel expenses, invitations, etc... They also would like to purchase a computer at the cutting edge of technology in order to perform numerical simulations (this would be a significant help in Modelling the velocity fied in turbulence).