Multicoloured Hardcore Model: Fast Mixing and Queueing
<|reference_start|>Multicoloured Hardcore Model: Fast Mixing and Queueing: We extend the hardcore model to a multicoloured version: a subset of vertices of a graph are coloured such that no vertex is adjacent to one of the same colour; uncoloured vertices do not constrain neighbours. This mathematically models multi-channel resource sharing, such as fibreoptic routing.   We analyse certain simple Glauber-type dynamics on such configurations, and find conditions which ensure fast mixing. These dynamics model a queueing system: customers queue for service at vertices, who only serve customers whilst they are coloured in the underlying configuration; uncoloured vertices sit idle. The mixing estimates are applied to control queue lengths in equilibrium.<|reference_end|>
@article{olesker-taylor2024multicoloured,
    title={Multicoloured Hardcore Model: Fast Mixing and Queueing},
    author={Sam Olesker-Taylor},
    journal={35th International Conference on Probabilistic, Combinatorial and
  Asymptotic Methods for the Analysis of Algorithms (AofA 2024) Volume 302, pp.
  20:1-20:14},
    year={2024},
    doi={10.4230/LIPIcs.AofA.2024.20},
    archivePrefix={arXiv},
    eprint={2406.14376},
    primaryClass={math.PR cs.DM}
}