Circular support in random sorting networks

Duncan Dauvergne, Bálint Virág

Research output: Contribution to journalArticle

Abstract

A sorting network is a shortest path from 12···n to n···21 in the Cayley graph of the symmetric group generated by adjacent transpositions. For a uniform random sorting network, we prove that in the global limit, particle trajectories are supported on π-Lipschitz paths. We show that the weak limit of the permutation matrix of a random sorting network at any fixed time is supported within a particular ellipse. This is conjectured to be an optimal bound on the support. We also show that in the global limit, trajectories of particles that start within distance #x220A; of the edge are within √2#x220A; of a sine curve in uniform norm.

Original languageEnglish (US)
Pages (from-to)1529-1553
Number of pages25
JournalTransactions of the American Mathematical Society
Volume373
Issue number3
DOIs
StatePublished - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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