Maximal Height Scaling of Kinetically Growing Surfaces
Maximal Height Scaling of Kinetically Growing Surfaces
The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: ${h}_{L}^{*}\ensuremath{\sim}{L}^{\ensuremath{\alpha}}$. For large values its distribution obeys $\mathrm{log}P({h}_{L}^{*})\ensuremath{\sim}\ensuremath{-}A({h}_{L}^{*}{/L}^{\ensuremath{\alpha}}{)}^{a}$. In the early-time regime where the …