An upper bound on the size of avoidance couplings
Abstract
We show that a coupling of noncolliding simple random walkers on the complete graph on $n$ vertices can include at most $n  \log n$ walkers. This improves the only previously known upper bound of $n2$ due to Angel, Holroyd, Martin, Wilson, and Winkler ({\it Electron.~Commun.~Probab.~18}, 2013). The proof considers couplings of i.i.d.~sequences of Bernoulli random variables satisfying a similar avoidance property, for which there is separate interest. Our bound in this setting should be closer to optimal.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.00210
 arXiv:
 arXiv:1712.00210
 Bibcode:
 2017arXiv171200210B
 Keywords:

 Mathematics  Probability;
 60J10;
 05C81
 EPrint:
 8 pages