Stochastic analysis on the phase separating random interface

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Under the situation that two distinct pure phases coexist in space like water/ice at zero temperature, hypersurfaces called interfaces are formed and separate these distinct phases at the microscopic level. In this research, we considered the ∇φ interface model as an equilibrium model of such interface and studied mainly asymptotic behaviors of the interface interacting with the wall. Especially, we obtained mathematically rigorous and precise results which were previously obtained by several heuristic arguments.