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The Euclidean Matching Problem

Gabriele Sicuro (Autor)

Buch | Hardcover

XIV, 136 Seiten

2016 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-46576-0 (ISBN)

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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.

Gabriele Sicuro is a postdoctoral researcher at the Centro Brasileiro de Pesquisas Físicas, in Rio de Janeiro. Born in 1987, he obtained his master degree in Physics at University of Salento, in Lecce, in 2011 and then his doctorate in Physics at University of Pisa in January 2015.

Introduction.- Optimisation, Disorder and Statistical Mechanics.- Euclidean Matching Problems.- Conclusions.

Erscheinungsdatum	12.11.2016
Reihe/Serie	Springer Theses
Zusatzinfo	XIV, 136 p. 50 illus., 6 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	Bipartite Matching Problem • Cavity Method • Convex Cost Functionals • Dynamics and statics • Euclidean Matching Problem • Euclidean Optimization Problem • Mathematical methods in physics • Mathematical Physics • Physics and Astronomy • Random Optimization Problem • Replica Trick • Statistical Physics • Statistical Physics, Dynamical Systems and Complex
ISBN-10	3-319-46576-7 / 3319465767
ISBN-13	978-3-319-46576-0 / 9783319465760
Zustand	Neuware