Central limit theorem for the determinantal point process with the confluent hypergeometric kernel

We consider the convergence of additive functionals under the determinantal point process with the confluent hypergeometric kernel, corresponding to a sufficiently smooth function $f(x\mathrm{/}R)$, as $R\to \mathrm{\infty }$. We show that these functionals approach Gaussian distribution and give an estimate on the Kolmogorov-Smirnov distance. To obtain these results, we derive an exact identity for expectations of multiplicative functionals in terms of Fredholm determinants.