We analyze the statistics of electrostatic energies (and their differences)
for a quantum dot system composed of a finite number K of electron islands
(metallic grains) with random capacitance-inductance matrix C, for which the
total charge is discrete, Q=Ne (where e is the charge of an electron and
N is an integer). The analysis is based on a generalized charging model,
where the electrons are distributed among the grains such that the
electrostatic energy E(N) is minimal. Its second difference (inverse
compressibility) χN=E(N+1)−2E(N)+E(N−1) represents the spacing between
adjacent Coulomb blockade peaks appearing when the conductance of the quantum
dot is plotted against gate voltage. The statistics of this quantity has been
the focus of experimental and theoretical investigations during the last two
decades. We provide an algorithm for calculating the distribution function
corresponding to χN and show that this function is piecewise
polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract
and Introduction