03538nam 22006495 450 991014885340332120200703045941.0978331946577710.1007/978-3-319-46577-7(CKB)3710000000918166(DE-He213)978-3-319-46577-7(MiAaPQ)EBC4723625(PPN)196322588(EXLCZ)99371000000091816620161024d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierThe Euclidean Matching Problem /by Gabriele Sicuro1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XIV, 136 p. 50 illus., 6 illus. in color.) Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053"Doctoral Thesis accepted by The University of Pisa, Italy."3-319-46576-7 3-319-46577-5 Includes bibliographical references at the end of each chapters.Introduction -- Optimisation, Disorder and Statistical Mechanics -- Euclidean Matching Problems -- Conclusions.This thesis discusses the random Euclidean bipartite matching problem, i.e., the matching problem between two different sets of points randomly generated on the Euclidean domain. The presence of both randomness and Euclidean constraints makes the study of the average properties of the solution highly relevant. The thesis reviews a number of known results about both matching problems and Euclidean matching problems. It then goes on to provide a complete and general solution for the one dimensional problem in the case of convex cost functionals and, moreover, discusses a potential approach to the average optimal matching cost and its finite size corrections in the quadratic case. The correlation functions of the optimal matching map in the thermodynamical limit are also analyzed. Lastly, using a functional approach, the thesis puts forward a general recipe for the computation of the correlation function of the optimal matching in any dimension and in a generic domain. iv>.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053PhysicsStatistical physicsDynamicsMathematical physicsMathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Physics.Statistical physics.Dynamics.Mathematical physics.Mathematical Methods in Physics.Complex Systems.Mathematical Physics.Statistical Physics and Dynamical Systems.511.66Sicuro Gabrieleauthttp://id.loc.gov/vocabulary/relators/aut477932MiAaPQMiAaPQMiAaPQBOOK9910148853403321The Euclidean Matching Problem2169040UNINA