First-passage time statistics for non-linear diffusion

Przemysław Chełminiak

Physica A: Statistical Mechanics and its Applications, 2024, vol. 633, issue C

Abstract: Most processes examined from a standpoint of the first-passage problem are modeled by linear diffusion equations. Here, we consider the non-linear diffusion equation in which diffusivity is power-law dependent on the concentration/probability density and explore its fundamental first-passage properties. Depending on the value of the power-law exponent, we demonstrate the exact and approximate expressions for the survival probability and the first-passage time distribution along with their asymptotic representations. These results refer to the freely and harmonically trapped diffusing particle. While in the former case the mean first-passage time is divergent, albeit the first-passage time distribution is normalized to unity, it is finite in the latter. To support this result, we derive the exact formula for the mean first-passage time to the target prescribed in the minimum of the harmonic potential.

Keywords: Non-linear diffusion; Survival probability; First-passage time distribution; Mean first-passage time; Harmonic potential (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:633:y:2024:i:c:s0378437123009251

DOI: 10.1016/j.physa.2023.129370

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