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PreprintarXiv licencearXiv

First Passage in the Presence of Jump Rate Fluctuations: A Transition from Infinite to Finite Mean

  • Bara Levit
  • Shlomi Reuveni
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Abstract

A simple symmetric random walk on a one-dimensional lattice is guaranteed to reach any target site, yet its mean first-passage time diverges. Here, we show that stochastic fluctuations in the jump rate can fundamentally alter this classic result. We find a phase transition in the mean first-passage time: sufficiently broad rate fluctuations render it finite, whereas weaker fluctuations leave it infinite. Our results demonstrate that temporal fluctuations in the jump rate---and hence in the diffusivity---can overcome spatial wandering and regularize otherwise divergent first-passage times.

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Cite

BibTeXRIS
BibTeX
@misc{levit2026first,
  title = {{First Passage in the Presence of Jump Rate Fluctuations: A Transition from Infinite to Finite Mean}},
  author = {Bara Levit and Shlomi Reuveni},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26925},
  eprint = {2609.26925},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26925},
}
RIS
TY  - UNPB
TI  - First Passage in the Presence of Jump Rate Fluctuations: A Transition from Infinite to Finite Mean
AU  - Bara Levit
AU  - Shlomi Reuveni
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26925
UR  - https://arxiv.org/abs/2609.26925
AB  - A simple symmetric random walk on a one-dimensional lattice is guaranteed to reach any target site, yet its mean first-passage time diverges. Here, we show that stochastic fluctuations in the jump rate can fundamentally alter this classic result. We find a phase transition in the mean first-passage time: sufficiently broad rate fluctuations render it finite, whereas weaker fluctuations leave it infinite. Our results demonstrate that temporal fluctuations in the jump rate---and hence in the diffusivity---can overcome spatial wandering and regularize otherwise divergent first-passage times.
ER  -