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PreprintCC BY 4.0arXiv

The Dynamical Bead Model

  • Giuseppe Cannizzaro
  • Harry Giles
  • Fabio Toninelli
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Abstract

We construct an infinite-dimensional diffusion on the space of interlaced particle configurations on Z x R, a process we call the dynamical bead model. The process (self-)interacts through instantaneous reflection and preserves the bead measures of [C. Boutillier, Ann. Probab., 2009]. Through the height function correspondence, our process is equivalent to a reversible interface in (2+1) dimensions. We provide compelling evidence that at large space-time scales the interface exhibits diffusive behaviour, as we compute exactly its diffusivity matrix and show it is non-degenerate and independent of time.

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Cite

BibTeXRIS
BibTeX
@misc{cannizzaro2026dynamical,
  title = {{The Dynamical Bead Model}},
  author = {Giuseppe Cannizzaro and Harry Giles and Fabio Toninelli},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25348},
  eprint = {2610.25348},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25348},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Dynamical Bead Model
AU  - Giuseppe Cannizzaro
AU  - Harry Giles
AU  - Fabio Toninelli
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25348
UR  - https://arxiv.org/abs/2610.25348
AB  - We construct an infinite-dimensional diffusion on the space of interlaced particle configurations on Z x R, a process we call the dynamical bead model. The process (self-)interacts through instantaneous reflection and preserves the bead measures of [C. Boutillier, Ann. Probab., 2009]. Through the height function correspondence, our process is equivalent to a reversible interface in (2+1) dimensions. We provide compelling evidence that at large space-time scales the interface exhibits diffusive behaviour, as we compute exactly its diffusivity matrix and show it is non-degenerate and independent of time.
ER  -