---
DOAJ_listed: '1'
OA_place: repository
OA_type: gold
_id: '18951'
abstract:
- lang: eng
  text: "We consider local dynamics of the dimer model (perfect matchings) on hypercubic
    boxes [n] \r\nd . These consist of successively switching the dimers along alternating
    cycles of prescribed (small) lengths. We study the connectivity properties of
    the dimer configuration space equipped with these transitions. Answering a question
    of Freire, Klivans, Milet, and Saldanha, we show that in three dimensions any
    configuration admits an alternating cycle of length at most 6. We further establish
    that any configuration on [n] d  features order n d−2  alternating cycles of length
    at most 4d−2. We also prove that the dynamics of dimer configurations on the unit
    hypercube of dimension d is ergodic when switching alternating cycles of length
    at most 4d−4. Finally, in the planar but non-bipartite case, we show that parallelogram-shaped
    boxes in the triangular lattice are ergodic for switching alternating cycles of
    lengths 4 and 6 only, thus improving a result of Kenyon and Rémila, which also
    uses 8-cycles. None of our proofs make reference to height functions."
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Ivailo
  full_name: Hartarsky, Ivailo
  last_name: Hartarsky
- first_name: Lyuben
  full_name: Lichev, Lyuben
  id: 9aa8388e-d003-11ee-8458-c4c1d7447977
  last_name: Lichev
- first_name: Fabio Lucio
  full_name: Toninelli, Fabio Lucio
  last_name: Toninelli
citation:
  ama: Hartarsky I, Lichev L, Toninelli FL. Local dimer dynamics in higher dimensions.
    <i>Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions</i>.
    2024. doi:<a href="https://doi.org/10.4171/aihpd/200">10.4171/aihpd/200</a>
  apa: Hartarsky, I., Lichev, L., &#38; Toninelli, F. L. (2024). Local dimer dynamics
    in higher dimensions. <i>Annales de l’Institut Henri Poincaré D, Combinatorics,
    Physics and Their Interactions</i>. EMS Press. <a href="https://doi.org/10.4171/aihpd/200">https://doi.org/10.4171/aihpd/200</a>
  chicago: Hartarsky, Ivailo, Lyuben Lichev, and Fabio Lucio Toninelli. “Local Dimer
    Dynamics in Higher Dimensions.” <i>Annales de l’Institut Henri Poincaré D, Combinatorics,
    Physics and Their Interactions</i>. EMS Press, 2024. <a href="https://doi.org/10.4171/aihpd/200">https://doi.org/10.4171/aihpd/200</a>.
  ieee: I. Hartarsky, L. Lichev, and F. L. Toninelli, “Local dimer dynamics in higher
    dimensions,” <i>Annales de l’Institut Henri Poincaré D, Combinatorics, Physics
    and their Interactions</i>. EMS Press, 2024.
  ista: Hartarsky I, Lichev L, Toninelli FL. 2024. Local dimer dynamics in higher
    dimensions. Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and
    their Interactions.
  mla: Hartarsky, Ivailo, et al. “Local Dimer Dynamics in Higher Dimensions.” <i>Annales
    de l’Institut Henri Poincaré D, Combinatorics, Physics and Their Interactions</i>,
    EMS Press, 2024, doi:<a href="https://doi.org/10.4171/aihpd/200">10.4171/aihpd/200</a>.
  short: I. Hartarsky, L. Lichev, F.L. Toninelli, Annales de l’Institut Henri Poincaré
    D, Combinatorics, Physics and Their Interactions (2024).
date_created: 2025-01-29T10:57:09Z
date_published: 2024-08-26T00:00:00Z
date_updated: 2025-07-08T08:39:55Z
day: '26'
department:
- _id: MaKw
doi: 10.4171/aihpd/200
external_id:
  arxiv:
  - '2304.10930'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2304.10930
month: '08'
oa: 1
oa_version: Preprint
publication: Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their
  Interactions
publication_identifier:
  eissn:
  - 2308-5835
  issn:
  - 2308-5827
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local dimer dynamics in higher dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...