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PreprintCC BY 4.0arXiv

Microscopic sorting in a multispecies exclusion process

  • Balázs Maga
  • Bálint Tóth
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Abstract

We study a one-dimensional multispecies TASEP model with each particle type having an associated speed parameter and faster particles overtaking slower ones with the rate being the positive part of their speed difference. After expressing the sorting time of a finite system given a reverse-speed initial condition as the maximum of sorting times for all different fast-slow cuts, we prove that forbidding fast-fast and slow-slow overtakes does not alter the law of the sorting time. This allows for an LPP formulation and an analytic expression of the sorting time.

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Cite

BibTeXRIS
BibTeX
@misc{maga2026microscopic,
  title = {{Microscopic sorting in a multispecies exclusion process}},
  author = {Balázs Maga and Bálint Tóth},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08135},
  eprint = {2610.08135},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08135},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Microscopic sorting in a multispecies exclusion process
AU  - Balázs Maga
AU  - Bálint Tóth
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08135
UR  - https://arxiv.org/abs/2610.08135
AB  - We study a one-dimensional multispecies TASEP model with each particle type having an associated speed parameter and faster particles overtaking slower ones with the rate being the positive part of their speed difference. After expressing the sorting time of a finite system given a reverse-speed initial condition as the maximum of sorting times for all different fast-slow cuts, we prove that forbidding fast-fast and slow-slow overtakes does not alter the law of the sorting time. This allows for an LPP formulation and an analytic expression of the sorting time.
ER  -