S. Becker

Spectral gaps for mean-field Coulomb gases

We prove a Poincar\'e inequality, uniform in the particle number, for repulsive (one-component) Coulomb gases in dimensions $d\ge3$, with inverse temperature $\beta_N$ that is allowed to depend on $N$. We assume a weak-coupling condition expressed in terms of the effective interaction strength $\Theta_N$ seen by a sing...