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PreprintCC BY 4.0arXiv

Random $3$-regular graphs are not globally synchronizing

  • Ciro Carvallo
  • Pablo Groisman
  • Dieter Mitsche
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Abstract

We study the homogeneous Kuramoto model on random 3-regular graphs. A connected graph G is globally synchronizing if, for almost every initial condition, the gradient flow converges to a fully synchronized state, in which all phases coincide. It has been conjectured by Bandeira [Oberwolfach Rep. 21 (2024) 1163-1226] that a random 3-regular graph G2n,3 is globally synchronizing with high probability. We disprove this conjecture in a strong way: G2n,3 is not globally synchronizing with probability tending to 1.

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Cite

BibTeXRIS
BibTeX
@misc{carvallo2026random,
  title = {{Random $3$-regular graphs are not globally synchronizing}},
  author = {Ciro Carvallo and Pablo Groisman and Dieter Mitsche},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09135},
  eprint = {2610.09135},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09135},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Random $3$-regular graphs are not globally synchronizing
AU  - Ciro Carvallo
AU  - Pablo Groisman
AU  - Dieter Mitsche
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.09135
UR  - https://arxiv.org/abs/2610.09135
AB  - We study the homogeneous Kuramoto model on random 3-regular graphs. A connected graph G is globally synchronizing if, for almost every initial condition, the gradient flow converges to a fully synchronized state, in which all phases coincide. It has been conjectured by Bandeira [Oberwolfach Rep. 21 (2024) 1163-1226] that a random 3-regular graph G_2n,3 is globally synchronizing with high probability. We disprove this conjecture in a strong way: G_2n,3 is not globally synchronizing with probability tending to 1.
ER  -