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Peer-reviewedCC BY 4.0Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions

Wall-crossing phenomenon for the liquid bin model

  • Sanjay Ramassamy
  • Benjamin Terlat
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Abstract

We introduce the liquid bin model as a continuous-time deterministic dynamics, arising as the hydrodynamic limit of a discrete-time stochastic interacting particle system called the infinite bin model. For the liquid bin model, we prove the existence and uniqueness of a stationary evolution, to which the dynamics converges exponentially fast. The speed of the front of the system is explicitly computed as a continuous piecewise rational function of the parameters of the model, revealing an underlying wall-crossing phenomenon. We show that the regions on which the speed is rational are of non-empty interior and are naturally indexed by Dyck paths. We provide a complete description of the adjacency structure of these regions, which generalizes the Stanley lattice for Dyck paths. Finally we point out an intriguing connection to the topic of extensions of partial cyclic orders to total cyclic orders.

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Cite

BibTeXRIS
BibTeX
@article{ramassamy2026wallcrossing,
  title = {{Wall-crossing phenomenon for the liquid bin model}},
  author = {Sanjay Ramassamy and Benjamin Terlat},
  journal = {Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05016091v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Wall-crossing phenomenon for the liquid bin model
AU  - Sanjay Ramassamy
AU  - Benjamin Terlat
PY  - 2026
DA  - 2026/09/28
JO  - Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions
UR  - https://hal.science/hal-05016091v2
AB  - We introduce the liquid bin model as a continuous-time deterministic dynamics, arising as the hydrodynamic limit of a discrete-time stochastic interacting particle system called the infinite bin model. For the liquid bin model, we prove the existence and uniqueness of a stationary evolution, to which the dynamics converges exponentially fast. The speed of the front of the system is explicitly computed as a continuous piecewise rational function of the parameters of the model, revealing an underlying wall-crossing phenomenon. We show that the regions on which the speed is rational are of non-empty interior and are naturally indexed by Dyck paths. We provide a complete description of the adjacency structure of these regions, which generalizes the Stanley lattice for Dyck paths. Finally we point out an intriguing connection to the topic of extensions of partial cyclic orders to total cyclic orders.
SN  - 2308-5827
SN  - 2308-5835
ER  -