Keynote speaker

Theory of stabilizing functionals, so far developed mainly in the context of binomial and Poisson input fields (Baryshnikov, Penrose, Yukich et al.), proved to be a strong and useful tool in many areas of applied probability. In particular, when combined with the so-called objective method, it provides a unified framework for establishing limit theorems (laws of large numbers, central limit theorems, large and moderate deviations) for a wide range of geometric functionals (broad class of random graphs and networks, random packing and deposition, Boolean models, spacing statistics, stochastic quantization), with the limiting characteristics (expectation, variance, relative entropy density) explicitly expressed in terms of the local geometry of the field. In this talk we show how these results can be extended to cover a general class of Gibbs input fields away from their phase transition regime (which is an indispensible assumption because the limit behavior at criticality is known to often violate the classical limit theory). The particular feature of our approach is that it is based on windowed perfect simulation schemes from thermodynamic limit, in the spirit of Fernandez, Ferrari and Garcia, involving subcritical directed percolation based bounds for decay of dependencies, which enables us to establish our limit results in purely geometric terms thus fully preserving the direct links between the limit characteristics and the local geometry of both the stabilizing functional considered and the interaction present in the Gibbsian input field. Last but not least, the algorithmic features of our proofs provide natural and efficient perfect simulation tools allowing for numeric evaluation of limit constants Talk based on joint work with J.E. Yukich