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math-ph2025
Simple analyticity criteria for repulsive multi-body potentials
Tyler Helmuth, Marcus Pappik, Will Perkins
We prove a simple, explicit lower bound on the radius of a zero-free disk for Gibbs point processes defined by finite-range, repulsive multi-body interactions. Our lower bound impr…
math.ST2025
Testing Thresholds and Spectral Properties of High-Dimensional Random Toroidal Graphs via Edgeworth-Style Expansions
Samuel Baguley, Andreas Göbel, Marcus Pappik +1
We study high-dimensional random geometric graphs (RGGs) of edge-density with vertices uniformly distributed on the -dimensional torus and edges inserted between sufficientl…
math.PR2025
Gradually Declining Immunity Retains the Exponential Duration of Immunity-Free Diffusion
Andreas Göbel, Nicolas Klodt, Martin S. Krejca +1
Diffusion processes pervade numerous areas of AI, abstractly modeling the dynamics of exchanging, oftentimes volatile, information in networks. A central question is how long the i…