Checking the Gaussian Correlation Conjecture

Goal:

Check numerically the so-called Gaussian Product Conjecture, claiming that, for any centered Gaussian vector N=(N1, ..., Nd) and any integer k>0, the quantity E[N12k... Nd2k] is always bigger than E[N12k]...E[Nd2k], irrespective of the covariance matrix of N.

Schedule: To be determined with the student(s).

Supervisors: Ivan Nourdin, Diu Tran, Guangqu Zheng.

Difficulty level: Advanced level.

Tools: Programs will be coded in Matlab or Scilab.

Results: [To be completed at the end of the project.]

FSCT -- University of Luxembourg