Finite-time blowup of a Brownian particle in a repulsive potential

P. L. Krapivsky; Baruch Meerson

doi:10.1103/1hds-9ttg

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arXiv · 2502.11796

Finite-time blowup of a Brownian particle in a repulsive potential

P. L. Krapivsky·Baruch Meerson

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Abstract

We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. We determine the average blowup time and study the probability distribution of the blowup time. In particular, we show that the long-time tail of this probability distribution decays purely exponentially, while the short-time tail exhibits an essential singularity. These qualitative features turn out to be quite universal, as they occur for all rapidly growing power-law potentials in arbitrary spatial dimensions. The quartic potential is especially tractable, and we analyze it in more detail.

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P. L. Krapivsky, Baruch Meerson. 2025-02-17. Finite-time blowup of a Brownian particle in a repulsive potential. https://doi.org/10.1103/1hds-9ttg

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