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The Inverse Mean First-Passage Time Problem
Abstract
We consider the mean first-passage time τ(x) for an overdamped particle in a one-dimensional potential landscape, and address the problem inverse to the textbook one: Given τ(x) as a function of starting distance, we look for a potential that realizes it. We derive the conditions on τ(x) under which such a potential exists. We show that while the power-law dependences τ(x)∼ xα with α≤ 2 may be realized by monotonic potentials, any realizable τ(x) with superquadratic growth requires potential wells arbitrarily far from the target; α= 2 separates sliding from trapping-dominated motion regimes.
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BibTeX
@misc{keidar2026inverse,
title = {{The Inverse Mean First-Passage Time Problem}},
author = {Tommer D. Keidar and Shlomi Reuveni and Igor M. Sokolov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03831},
eprint = {2611.03831},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03831},
}
RIS
TY - UNPB
TI - The Inverse Mean First-Passage Time Problem
AU - Tommer D. Keidar
AU - Shlomi Reuveni
AU - Igor M. Sokolov
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03831
UR - https://arxiv.org/abs/2611.03831
AB - We consider the mean first-passage time τ(x) for an overdamped particle in a one-dimensional potential landscape, and address the problem inverse to the textbook one: Given τ(x) as a function of starting distance, we look for a potential that realizes it. We derive the conditions on τ(x) under which such a potential exists. We show that while the power-law dependences τ(x)∼ x^α with α≤ 2 may be realized by monotonic potentials, any realizable τ(x) with superquadratic growth requires potential wells arbitrarily far from the target; α= 2 separates sliding from trapping-dominated motion regimes.
ER -