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Random walkers absorbing on a boundary sample the Harmonic Measure linearlyand independently: we discuss how the recurrence times between impacts enablenon-linear moments of the measure to be estimated. From this we derive a newtechnique to simulate Dielectric Breakdown Model growth which is governednonlinearly by the Harmonic Measure. Recurrence times are shown to be accurateand effective in probing the multifractal growth measure of diffusion limitedaggregation. For the Dielectric Breakdown Model our new technique grows largeclusters efficiently and we are led to significantly revise earlier exponentestimates. Previous results by two conformal mapping techniques were lessconverged than expected, and in particular a recent theoretical suggestion ofsuperuniversality is firmly refuted.Comment: 9 pages, 8 figure

Growth by random walker sampling and scaling of the dielectric breakdown model