Papers › Hyperuniform and rigid stable matchings
Hyperuniform and rigid stable matchings
Michael Andreas Klatt, Günter Last, D. Yogeshwaran
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We study a stable partial matching τ of the (possibly randomized) d-dimensional lattice with a stationary determinantal point process Ψ on ℝᵈ 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 behaviour. For hyperuniformity, we also additionally need to assume some mixing condition on Ψ. Further, if Ψ is a Poisson process then Ψ^τ has an exponentially decreasing truncated pair correlation function.
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