Enhanced Interface Repulsion from Quenched Hard–wall Randomness

  title={Enhanced Interface Repulsion from Quenched Hard–wall Randomness},
  author={Giambattista Giacomin}
We consider the harmonic crystal, or massless free field, ϕ = {ϕx} x∈Z d , d ≥ 3, that is the centered Gaussian field with covariance given by the Green function of the simple random walk on Z d. Our main aim is to obtain quantitative information on the repulsion phenomenon that arises when we condition ϕx to be larger than σx, σ = {σx} x∈Z d is an IID field (which is also independent of ϕ), for every x in a large region DN = N D ∩ Z d , with N a positive integer and D ⊂ R d a rather general… CONTINUE READING