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Condensation and metastability in the supercritical two-species zero-range process via resolvent and H1-approximation

  • Seonwoo Kim
  • Seungchan Lee
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Abstract

In this article, we investigate the two-species zero-range process, a multi-species generalization of the classical zero-range process. First, we analyze its condensation regime, which directly parallels its single-species counterpart. As our main result, we establish the dynamical metastable behavior of the location of the single condensate, showing that its motion is governed by a simple Markov chain on the accelerated time scale N1+α, where N denotes the total number of particles in the system and the parameter α>1 governs the attractivity of the system. Another novelty of this work lies in the proof technique, which integrates the recently developed resolvent approach with the H1-approximation method to rigorously characterize metastability.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026condensation,
  title = {{Condensation and metastability in the supercritical two-species zero-range process via resolvent and $H^1$-approximation}},
  author = {Seonwoo Kim and Seungchan Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03821},
  eprint = {2609.03821},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03821},
}
RIS
TY  - UNPB
TI  - Condensation and metastability in the supercritical two-species zero-range process via resolvent and H^1-approximation
AU  - Seonwoo Kim
AU  - Seungchan Lee
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03821
UR  - https://arxiv.org/abs/2609.03821
AB  - In this article, we investigate the two-species zero-range process, a multi-species generalization of the classical zero-range process. First, we analyze its condensation regime, which directly parallels its single-species counterpart. As our main result, we establish the dynamical metastable behavior of the location of the single condensate, showing that its motion is governed by a simple Markov chain on the accelerated time scale N^1+α, where N denotes the total number of particles in the system and the parameter α>1 governs the attractivity of the system. Another novelty of this work lies in the proof technique, which integrates the recently developed resolvent approach with the H^1-approximation method to rigorously characterize metastability.
ER  -