Statistical Properties of Random Interface System

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Abstract
Statistical properties of binary phase system with semi-macroscopic random interfaces are studied. Singularity and symmetry of the correlation function are discussed in the case of smooth interface. Characteristic length scales are defined by using the interface statistics. The existence of the equivalent sphere system is shown for the non-spherical irregular droplet. The irregularity of simple droplets is characterized by an inequality related to the topological invariant. It is shown that statistically self-complementary, smooth system is mutually percolating. As a statistical foundation of the random interface problem, the relations to the theory of excursion set of random field are discussed. The expression of area density of the boundary set is obtained for the Gaussian field in Euclidean space with arbitrary dimension d. The cross-over phenomena in the spinodal decomposition process is also discussed using the statistical analyses on the interface.

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