A diffusion approximation for systems with frequent weak resetting
Tobias Galla
Submitted (2026)
Submitted (2026)
We develop a diusion approximation for systems subject to fast random resetting by small ampli- tudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing the stationary distribution and mean rst-passage times of simple one-dimensional systems. The approximation captures dynamically induced corre- lations in multi-particle systems, and it can be used to generalise the conditionally independent and identically distributed structure recently found in systems with full resetting. Finally, we show that resetting can induce cycles and patterns, which can be characterised using the diusion approxima- tion.
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