We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach in Hofer-Temmel (2019) and Hofer-Temmel and Houdebert (2019) we will use this to couple two finite Gibbs processes with different boundary conditions. As one application we will establish Poisson approximation of point processes derived from certain infinite volume repulsive Gibbs processes via dependent thinning. As another application we shall discuss empty space probabilities of certain Gibbs processes.
Domination Between Trees and Application to an Explosion Problem
Convergence rates for rank-based models with applications to portfolio theory
Convergence to equilibrium for finite Markov processes, with application to the Random Energy Model
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