P. Le Doussal

Linear statistics in the Coulomb gas: cumulants beyond rotational invariance

We consider a classical Coulomb gas of $N$ particles in dimension $d\geq2$, confined by a general external potential $U$ in the large-$N$ limit. In that limit the density of particles has a compact support called the droplet. We study smooth linear statistics ${\mathcal L}_N=\sum_{i=1}^N f({\bf x}_i)$ at large $N$. Whi...