Description

Gaussian multiplicative chaos is a beautiful theory of random measures, initiated by Kahane in the 1980s. It has since found applications in many areas, ranging from mathematical finance to turbulence. This project would be based on the construction and properties of these measures, extending to appications or further theory according to interest.

Prerequisites

3H Stochastic Processes is essential

Resources

For a quick overview see the article on multifractal random measures here.

Further reference material:

• I.Benjamini and O.Schramm, KPZ in One Dimensional Random Geometry of Multiplicative Cascades .
• J. Aru's blog on GMC
• R.Rhodes and V.Vargas Gaussian multiplicative chaos and applications: A review

Get in touch by email if you have questions.