Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Gibbs point process approximation: Total variation bounds using Stein's method

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.

Flavour-violation in two-Higgs-doublet models

In these proceedings we review the flavour phenomenology of 2HDMs with generic Yukawa structures [1]. We first consider the quark sector and find that despite the stringent constraints from FCNC processes large effects in tauonic B decays are still possible. We then consider lepton flavour observables, show correlations between m →eg and m− →e−e+e− in the 2HDM of type III and give upper bounds on the lepton flavour violating B decay Bd →me.