  We present a calculation for the second moment of the local density of states
in a model of a two-dimensional quantum dot array near the quantum Hall
transition. The quantum dot array model is a realistic adaptation of the
lattice model for the quantum Hall transition in the two-dimensional electron
gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and
Grinstein. We make use of a Dirac fermion representation for the Green
functions in the presence of fluctuations for the quantum dot energy levels. A
saddle-point approximation yields non-perturbative results for the first and
second moments of the local density of states, showing interesting fluctuation
behaviour near the quantum Hall transition. To our knowledge we discuss here
one of the first analytic characterizations of chaotic behaviour for a
two-dimensional mesoscopic structure. The connection with possible experimental
investigations of the local density of states in the quantum dot array
structures (by means of NMR Knight-shift or single-electron-tunneling
techniques) and our work is also established.
