  Arising as a fluctuation phenomenon, the equilibrium distribution of
meandering steps with mean separation $<\ell>$ on a "tilted" surface can be
fruitfully analyzed using results from RMT. The set of step configurations in
2D can be mapped onto the world lines of spinless fermions in 1+1D using the
Calogero-Sutherland model. The strength of the ("instantaneous",
inverse-square) elastic repulsion between steps, in dimensionless form, is
$\beta(\beta-2)/4$. The distribution of spacings $s< \ell>$ between neighboring
steps (analogous to the normalized spacings of energy levels) is well described
by a {\it "generalized" Wigner surmise}: $p_{\beta}(0,s) \approx a
s^{\beta}\exp(-b s^2)$. The value of $\beta$ is taken to best fit the data;
typically $2 \le \beta \le 10$. The procedure is superior to conventional
Gaussian and mean-field approaches, and progress is being made on formal
justification. Furthermore, the theoretically simpler step-step distribution
function can be measured and analyzed based on exact results. Formal results
and applications to experiments on metals and semiconductors are summarized,
along with open questions. (conference abstract)
