• Corpus ID: 245837539

Universality of cutoff for exclusion with reservoirs

@inproceedings{Salez2022UniversalityOC,
  title={Universality of cutoff for exclusion with reservoirs},
  author={Justin Salez},
  year={2022}
}

• J. Salez
• Published 10 January 2022
• Mathematics

We consider the exclusion process with reservoirs on arbitrary networks. We characterize the spectral gap, mixing time, and mixing window of the process, in terms of certain simple spectral statistics of the underlying network. Among other consequences, we establish a non-conservative analogue of Al-dous’s spectral gap conjecture, and we show that cutoff occurs if and only if the product condition is satisfied. We illustrate this by providing explicit cutoffs on discrete lattices of arbitrary dimensions and boundary conditions, which substantially generalize recent one-dimensional results. We also obtain cutoff phenomena in relative entropy, Hilbert norm, separation distance and supremum norm. Our proof exploits negative dependence in a novel, simple way to reduce the understanding of the whole process to that of single-site marginals. We believe that this approach will find other applications.