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Infinite volume asymptotics of the ground state energy in a scaled Poissonian potential. (English) Zbl 0996.82036
The authors investigate the ground state energy of the random Schrödinger operator \(-\frac{1}{2}\Delta+\beta (\log t)^{-2/d}V\) on the box \((-t,t)^{d}\) with Dirichlet boundary conditions. Here \(V\) is the Poissonian potential obtained by translation a fixed non-negative compactly supported shape function to all the particles of \(d\)-dimensional Poissonian point process, the scaling function \((\log t)^{-2/d}\) is determined by the typical size of the largest hole of the Poissonian cloud in the box \((-t,t)^{d}.\)

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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