Fluctuations of an atomic ledge bordering a crystalline facet

The statistical properties of border ledge fluctuations were investigated. It was shown that the border ledge of a crystalline facet has fluctuations of size l^1/3, much reduced in comparison with a simple random walk. It was claimed that the scaling form was universal within the class of surface models with short range interactions, and that the scaling function can be expressed through determinants of infinite dimensional matrices. In the scaling regime, the border ledge fluctuations were shown to be non-Gaussian and related to the edge statistics of Gaussian unitary ensemble multimatrix models.