Nonequilibrium statistics of harmonically trapped run-and-tumble particles: An exact convolution approach

What the math gives to ML

The paper gives an exact stationary decomposition for a harmonically confined run-and-tumble process: the position distribution is the convolution of an athermal persistent-noise distribution with an Ornstein-Uhlenbeck thermal kernel. Its shape is controlled by persistence relative to confinement and thermal noise relative to active diffusion, with a crossover from boundary-peaked non-Gaussian fluctuations to Gaussian-like fluctuations. A transferable neural-network mechanism is a persistent-noise optimizer whose local parameter fluctuations are calibrated using this convolution rather than modeled as purely white Gaussian noise. The most testable application is a local-basin optimizer or exploration module with an explicit prediction for parameter-distribution shape, variance, and the discrete stability boundary.