Spatial random field models inspired from statistical physics with applications in the geosciencesSpatial random field models inspired from statistical physics with applications in the geosciences Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-09-252006enThe spatial structure of fluctuations in spatially inhomogeneous processes can be modeled in terms of Gibbs random fields. A local low energy estimator (LLEE) is proposed for the interpolation (prediction) of such processes at points where observations are not available. The LLEE approximates the spatial dependence of the data and the unknown values at the estimation points by low-lying excitations of a suitable energy functional. It is shown that the LLEE is a linear, unbiased, non-exact estimator. In addition, an expression for the uncertainty (standard deviation) of the estimate is derivedhttp://creativecommons.org/licenses/by/4.0/Physica A: Statistical Mechanics and its Applications3651-2211-216 D.T. Hristopulos