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We present a calculation for the second moment of the local density of statesin a model of a two-dimensional quantum dot array near the quantum Halltransition. The quantum dot array model is a realistic adaptation of thelattice model for the quantum Hall transition in the two-dimensional electrongas in an external magnetic field proposed by Ludwig, Fisher, Shankar andGrinstein. We make use of a Dirac fermion representation for the Greenfunctions in the presence of fluctuations for the quantum dot energy levels. Asaddle-point approximation yields non-perturbative results for the first andsecond moments of the local density of states, showing interesting fluctuationbehaviour near the quantum Hall transition. To our knowledge we discuss hereone of the first analytic characterizations of chaotic behaviour for atwo-dimensional mesoscopic structure. The connection with possible experimentalinvestigations of the local density of states in the quantum dot arraystructures (by means of NMR Knight-shift or single-electron-tunnelingtechniques) and our work is also established.Comment: 11 LaTeX pages, 1 postscript figure, to appear in Phys.Rev.

Characterization of the local density-of-states fluctuations near the integer quantum Hall transition in a quantum-dot array