Junior Professor (W1)
Mathematical Stochastics, Department of Mathematics, Universität Hamburg
I work in probability theory, specifically on the fluctuations of random spatial structures such as random tessellations, random geometric graphs, continuum percolation and birth–growth models. Typical questions I study include how such fluctuations are distributed, how large their variance is, and how sensitive they are to small perturbations of the underlying randomness. The three main themes of my research are distributional approximation and Stein's method; superconcentration, chaos and noise sensitivity; and statistical applications, in particular to random forests and causal inference.
Prospective students. For enquiries about Bachelor’s, Master’s or PhD thesis under my supervision in probability theory, in particular stochastic geometry or Stein’s method, please contact me by email.
Matching estimators compare each treated unit with similar untreated ones and are among the most widely used tools for estimating average treatment effects (ATE) in causal inference. We prove Gaussian approximation bounds with explicit rates for covariate- and rank-based matching estimators, and justify a mutiplier bootstrap procedure for inference, using stabilization theory and the Malliavin–Stein method.
The generalized Dickman distribution appears as the limit of weighted sums in probabilistic number theory, the analysis of algorithms and random trees, to name a few. Using Stein’s method, we derive the first approximation bounds in the Kolmogorov distance, with applications to the runtime of the Quickselect algorithm and to the weighted depth in randomly grown simple increasing trees.
In scale-free networks a few vertices known as hubs have very large degrees. We determine the limiting distribution of the largest degrees in a class of inhomogeneous random graphs, and use it to prove consistency of the Hill estimator for the power-law exponent of the degree distribution.
Colour the cells of a Poisson–Voronoi tessellation black or white by fair coin flips: is there a black path crossing a large square from left to right, and does the answer survive if a small fraction of the points is resampled? We introduce a spectral point process for Poisson functionals, the continuum analogue of the spectral sample of a Boolean function, and use it to prove sharp noise sensitivity of crossing events in Poisson–Voronoi percolation and sharp noise instability in the critical Poisson Boolean model, under spatial birth–death dynamics.
A functional is superconcentrated if its variance is much smaller than classical bounds such as the Poincaré inequality predict. In a dense random geometric graph, for instance, inserting a single point changes the degrees of many vertices, yet the number of vertices of small degree fluctuates far less than this bound suggests. For Poisson functionals that are sums of local scores, we identify simple conditions that guarantee superconcentration, and hence chaos, meaning decorrelation under small perturbations by spatial birth–death dynamics. Applications include counts of small-degree vertices and isolated subgraphs in random geometric graphs, and crossing indicators in critical continuum percolation.
My research is supported by the German Research Foundation (DFG) through the Priority Programme “Random Geometric Systems” (SPP 2265), Project No. 531540467, and by the German Academic Exchange Service (DAAD), Project ID 57761484. Details