|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910148853403321 |
|
|
Autore |
Sicuro Gabriele |
|
|
Titolo |
The Euclidean Matching Problem / / by Gabriele Sicuro |
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 2017.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (XIV, 136 p. 50 illus., 6 illus. in color.) |
|
|
|
|
|
|
Collana |
|
Springer Theses, Recognizing Outstanding Ph.D. Research, , 2190-5053 |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Physics |
Statistical physics |
Dynamics |
Mathematical physics |
Mathematical Methods in Physics |
Complex Systems |
Mathematical Physics |
Statistical Physics and Dynamical Systems |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
"Doctoral Thesis accepted by The University of Pisa, Italy." |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references at the end of each chapters. |
|
|
|
|
|
|
Nota di contenuto |
|
Introduction -- Optimisation, Disorder and Statistical Mechanics -- Euclidean Matching Problems -- Conclusions. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
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 |
|
|
|
|