Djalil Chafaï

An optimal Poincar\'e inequality for the complex Ginibre log-gas

We establish an optimal Poincar\'e inequality for real-valued symmetric observables of the complex Ginibre log-gas. Equality is attained by the real and imaginary parts of the center-of-mass observable. Equivalently, we determine the exact spectral gap of the associated overdamped Langevin dynamics, for real symmetric...