Institute of Applied Analysis
University Ulm
Helmholtzstraße 18
89081 Ulm
Room E.10
Tel.: +49 731 50-23560
andre.schlichting@uni-ulm.de
University Ulm
Helmholtzstraße 18
89081 Ulm
Room E.10
Tel.: +49 731 50-23560
andre.schlichting@uni-ulm.de
News and Updates
Preprint: Formation of clusters and coarsening in weakly interacting diffusions
Together with Nicolai Gerber, Rishabh Gvalani, Martin Hairer and Greg Pavliotis, we study the clustering behavior of weakly interacting diffusions under the influence of sufficiently localized attractive interaction potentials on the one-dimensional torus. We describe how this clustering behavior is closely related to the presence of discontinuous phase transitions in the mean-field PDE. For local attractive interactions, we employ a new variant of the strict Riesz rearrangement inequality to prove that all global minimizers of the free energy are either uniform or single-cluster states, in the sense that they are symmetrically decreasing.Now published in Nonlinearity 39(7), 075023 (2026).
Preprint: Derivation of the fourth-order DLSS equation with nonlinear mobility via chemical reactions
Together with Alexander Mielke and Artur Stephan, we provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretized circle for a process in which pairs of particles occupying the same site simultaneously jump to the two neighboring sites; the reverse process involves pairs of particles at adjacent sites simultaneously jumping back to the site located between them. Depending on the rates, in the vanishing-mesh-size limit we obtain either the classical DLSS equation or a variant with nonlinear mobility of power type.Now accepted in SIAM Journal on Mathematical Analysis.
Preprint: Existence and Non-existence for Continuous Generalized Exchange-Driven Growth model
Together with Chun Yin Lam, after the derivation of the continuous generalized exchange-driven growth model in arXiv:2503.21572, we continue the study of the existence and uniqueness of solutions for kernels with superlinear growth at infinity and singularity at the origin. Moreover, we show the non-existence of solutions for kernels with sufficiently rapid growth. The latter result is shown via the finite-time gelation and instantaneous gelation in the sense of moment blow-up.
Preprint: Convergence of a stochastic particle system to the continuous generalized exchange-driven growth model
Together with Chun Yin Lam, we study the continuous generalized exchange-driven growth model (CGEDG) is a system of integro-differential equations describing the evolution of cluster mass under mass exchange. The rate of exchange depends on the masses of the clusters involved and the mass being exchanged. This can be viewed as both a continuous generalization of the exchange-driven growth model and a coagulation-fragmentation equation that generalizes the continuous Smoluchowski equation.Now published in Electron. J. Probab. 31(50), 1-29 (2026).