MaxEnt approach for the probabilistic modeling of matrix-valued random fields with constrained eigenvalues: application to apparent mechanical and transport properties
Résumé
This work is devoted to the construction of a class of prior stochastic models for non-Gaussian positive-definite matrix-valued random fields, having recourse to the maximum entropy (MaxEnt) principle. Specifically, the proposed approach aims at taking into account, in addition to usual constraints (e.g. normalization condition for the p.d.f., invertibility, etc.), some information related to the variances of some selected eigenvalues. After having recalled the general stochastic framework, we will present some mathematical derivations and discuss a few fundamental properties of the proposed class. It will be shown that the latter is basically parameterized by a set of spatial correlation lengths, a real-valued deterministic field controlling the overall level of statistical fluctuations and a Rm -valued deterministic field controlling the variances of m selected random eigenvalues. Computational issues, related in particular to random generation, will be discussed.