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DY: Fachverband Dynamik und Statistische Physik

DY 32: Nonlinear Stochastic Systems

DY 32.3: Vortrag

Donnerstag, 20. März 2025, 10:15–10:30, H43

Cross-correlation-response relations for systems driven by shot noise — •Jakob Stubenrauch and Benjamin Lindner — BCCN Berlin and Physics Department HU Berlin, Germany

In the analysis of stochastic dynamics, the Furutsu-Novikov [1,2] theorem (FNT), linking the input-output cross-correlation of a system driven by Gaussian noise to the response function of the system, has proven important in various applications.

In several situations, such as photon-detectors or neurons, it is inaccurate to model the input process as Gaussian noise; in the two examples the input is instead a sequence of pulses at random times (shot noise). Here, we present recently discovered analogues of the FNT for systems driven by shot noise [3]. Specifically, we show that the input-output cross-correlation of any system driven by Poissonian shot noise is linearly related to the linear response of the system to modulations of the intensity of input shots. We further present extensions for colored shot noise and for shot noise with random amplitudes.

To illustrate the wide applicability of our general result, we further present a fluctuation-response relation of a leaky integrate-and-fire neuron: Building on previous work [4], we show how the spontaneous output fluctuations of a spike-driven neuron are related to its susceptibility. Lastly, as teasers, we present applications to single-photon-detection, remote control in neural networks, and synaptic plasticity.

[1] Furutsu, J. Res. Natl. Bur. Stand. (1963) [2] Novikov, J. Exp. Theor. Phys. (1965) [3] Stubenrauch and Lindner, Phys. Rev. X (2024), [4] Lindner, Phys. Rev. Lett. (2022)

Keywords: Linear response theory; Path integral methods; Stochastic systems; Shot-noise driven systems; Spiking neurons