| Abstract: |
| We study the asymptotic behavior of large volume Gibbs measures associated with discrete Hamiltonians that are defined on deformations of a stationary stochastic lattice. Assuming polynomial growth and finite range interactions for the discrete Hamiltonian, we prove a large deviation principle with a continuum elasticity-type rate functional. We then investigate this functional in the small temperature regime. Under suitable continuity assumptions on the microscopic Hamiltonian, we show that it can be well approximated by the $\Gamma$-limit of the rescaled discrete Hamiltonians. |
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