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On misoriented ("vicinal") surfaces, the terrace-width (spacing between adjacent steps) distribution can be related to the spacing distribution of repelling spinless fermions in one dimension, and thence to generalizations of the Wigner surmise (GWS) from random-matrix theory. The GWS expression also emerges as the steady-state solution of a Fokker-Planck description of step evolution. Subsequently we applied this approach to the areas of proximity cells (capture zones) of islands and quantum dots on surfaces; going beyond mean-field is necessary to get the correct relation between the characteristic GWS exponent and the critical nucleus size. A fragmentation model offers further insights. I compare analyses of island-size distributions and of scaling of island density vs. flux. I discuss several computer simulations and various experimental examples. In particular, for 6P on mica we need a novel quantitative rate equation treatment of "hot precursors". Applications to social phenomena include the distribution of Metro stations in Paris and the areal distribution of secondary administrative units (e.g., Landkreise and arrondissements).

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Theodore L. Einstein, University of Maryland at College Park
Seminar Room TP 0.03
Contact: Joachim Krug