3 papers
math.AP2025
Existence, scaling, and spectral gap for traveling fronts in the 2D renormalized Allen--Cahn equation
Gideon Chiusole, Christian Kuehn
We study the deterministic skeleton of the renormalized stochastic Allen--Cahn equation in spatial dimension . For all sufficiently small regularization parameters , we con…
math.CO2025
Simplicial Complex Emergence on Directed Hypergraphs
Christian Kuehn, Fergal Murphy
We study when co-evolving (or adaptive) higher-order networks defined on directed hypergraphs admit a simplicial description. Binary and triadic couplings are modelled by time-depe…
math.DS2025
The Mean-Field Ott-Antonsen Manifold is an Unstable Manifold in the Continuum Limit
Christian Kuehn, Giacomo Landi
We study interacting particle systems of Kuramoto-type. Our focus is on the dynamical relation between the partial differential equation (PDE) arising in the continuum limit (CL) a…