Hyperuniform and rigid stable matchings. Issue 2 (27th April 2020)

• Record Type: Journal Article
• Authors: Andreas Klatt, Michael; Last, Günter; Yogeshwaran, D.
• Is Part Of: Random structures & algorithms. Volume 57:Issue 2(2020)
• Page Start: 439
• Page End: 473
• Publication Date: 2020-04-27
• Subjects: determinantal process -- hyperuniformity -- number rigidity -- pair correlation function -- Poisson process -- stable matching; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20923
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : We study a stable partial matching τ of the d ‐dimensional lattice with a stationary determinantal point process Ψ on R d with intensity α >1. For instance, Ψ might be a Poisson process. The matched points from Ψ form a stationary and ergodic (under lattice shifts) point process Ψ τ with intensity 1 that very much resembles Ψ for α close to 1. On the other hand Ψ τ is hyperuniform and number rigid, quite in contrast to a Poisson process. We deduce these properties by proving more general results for a stationary point process Ψ, whose so‐called matching flower (a stopping set determining the matching partner of a lattice point) has a certain subexponential tail behavior. For hyperuniformity, we also additionally need to assume some mixing condition on Ψ. Furthermore, if Ψ is a Poisson process then Ψ τ has an exponentially decreasing truncated pair correlation function.