In this talk, we will see how to find quantitative central limit theorems for functionals of a Poisson measure. The Malliavin-Stein method allows us to find speeds of convergence to Normality, just by estimating the cost of adding a point or two to the configuration. As an illustrative example, we will use the on-line nearest neighbour graph, a simple model for a network growing in time. The sum of power-weighted edge-lengths of this graph exhibits non-standard behaviour, and was conjectured in 2009 to satisfy a CLT. New so-called p-Poincaré inequalities allowed us to settle this conjecture, and we will talk about how to achieve, through them, a Malliavin-Stein bound with minimal moment assumptions.
Tara is a doctoral researcher at the University of Luxembourg.
Stein's method previous