Spectral Properties of Effective Dynamics from Conditional Expectations

Understand

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science.

• For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach.
• In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator.
• We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems.