We consider the random Euclidean assignment problem on the line between two sets of N random points, independently generated with the same probability density function ϱ. The cost of the matching is supposed to be dependent on a power p> 1 of the Euclidean distance of the matched pairs. We discuss an integral expression for the average optimal cost for N≫ 1 that generalizes a previous result obtained for p= 2. We also study the possible divergence of the given expression due to the vanishing of the probability density function. The provided regularization recipe allows us to recover the proper scaling law for the cost in the divergent cases, and possibly some of the involved coefficients. The possibility that the support of ϱ is a disconnected interval is also analysed. We exemplify the proposed procedure and we compare our predictions with the results of numerical simulations.

Caracciolo S., D'Achille M., Sicuro G. (2019). Anomalous Scaling of the Optimal Cost in the One-Dimensional Random Assignment Problem. JOURNAL OF STATISTICAL PHYSICS, 174(4), 846-864 [10.1007/s10955-018-2212-9].

Anomalous Scaling of the Optimal Cost in the One-Dimensional Random Assignment Problem

Sicuro G.
2019

Abstract

We consider the random Euclidean assignment problem on the line between two sets of N random points, independently generated with the same probability density function ϱ. The cost of the matching is supposed to be dependent on a power p> 1 of the Euclidean distance of the matched pairs. We discuss an integral expression for the average optimal cost for N≫ 1 that generalizes a previous result obtained for p= 2. We also study the possible divergence of the given expression due to the vanishing of the probability density function. The provided regularization recipe allows us to recover the proper scaling law for the cost in the divergent cases, and possibly some of the involved coefficients. The possibility that the support of ϱ is a disconnected interval is also analysed. We exemplify the proposed procedure and we compare our predictions with the results of numerical simulations.
2019
Caracciolo S., D'Achille M., Sicuro G. (2019). Anomalous Scaling of the Optimal Cost in the One-Dimensional Random Assignment Problem. JOURNAL OF STATISTICAL PHYSICS, 174(4), 846-864 [10.1007/s10955-018-2212-9].
Caracciolo S.; D'Achille M.; Sicuro G.
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/958763
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact