Speaker: Olav Kallenberg

Title: Inner and outer conditioning in point processes and particle systems

Abstract: A point process $\xi$ on a suitable space $S$ may be regarded as the model of a particle system in space. A basic problem is to study the conditional distribution of $\xi$ in a bounded set $B\subset S$, given the configuration of $\xi$ outside of $B$. In statistical mechanics, such studies go back to the fundamental work of J.W.\ Gibbs (1902), leading up to the theory of Gibbs measures. The merger of the physical and mathematical theories was initiated in the 1970's and 80's. In this talk I shall outline the elements of a general theory of conditioning, involving the notions of Palm and Gibbs kernels, obtained by dual disintegrations of a compound Campbell measure.