Statistics of the charging spectrum of a two-dimensional Coulomb-glass island

The fluctuations of capacitance of a two-dimensional island are studied in the regime of low electron concentration and strong disorder, when electrons can be considered classical particles. The universal capacitance distribution is found, with the dispersion being of the order of the average. This distribution is shown to be closely related to the shape of the Coulomb gap in the one-electron density of states of the island. Behavior of the capacitance fluctuations near the metal-insulator transition is discussed.