Large deviations and Young measures for a Poissonian model of biphased material (Q1578581)

The ideas of stochastic homogenization and Young measures are described in short. The model of Poissonian biphased material describes a biphased material whose irregularities have random scale and shape. This model is called Poisson blob model or Swiss cheese model in [\textit{R. Meester} and \textit{R. Roy}, ``Continuum percolations'' (1996; Zbl 0858.60092)] and discussed by \textit{A.-S. Sznitman} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 28, No. 3, 345-370 (1995; Zbl 0826.60018)]. For the random Young measures associated to the functions describing irregularities of the Poissonian biphased material, the large deviations principle ``à la Varadhan'' is proved in the space of bounded Borel measures endowed with the topology of the weak convergence.