Dresden 2026 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 7: Focus Session: Large Deviations and Rare Events I
DY 7.5: Talk
Monday, March 9, 2026, 10:45–11:00, ZEU/0114
Concentration of observables in slow-fast dynamical systems with noise — •Xizhu Zhao1,2 and Aljaž Godec1,2 — 1Mathematical Physics and Stochastic Dynamics, Institute of Physics, University of Freiburg, Freiburg, Germany — 2Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
Stochastic differential equations involving separated timescales play an important role in modeling the dynamics of complex systems in physics, biology, and climate science. We explore the concentration of observables, i.e. functions or functionals of dynamical variables, in slow-fast dynamical systems with noise. Using stochastic analysis and singular perturbation theory, we determine the domains of concentration for observables in systems with a stable manifold or undergoing a bifurcation. We also derive bounds for the distribution of the first-exit time from these domains. The results show that the concentration of observables exhibits behavior distinct from that of microscopic sample paths.
Keywords: stochastic differential equations; dynamical systems; concentration; first-exit time