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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-01092015-103245


Tipo di tesi
Tesi di dottorato di ricerca
Autore
SICURO, GABRIELE
URN
etd-01092015-103245
Titolo
The Euclidean Matching Problem
Settore scientifico disciplinare
FIS/02
Corso di studi
SCIENZE DI BASE "GALILEO GALILEI"
Relatori
tutor Prof. Caracciolo, Sergio
commissario Prof. Ricci-Tersenghi, Federico
commissario Prof. Vicari, Ettore
commissario Prof. Zecchina, Riccardo
commissario Prof. Konishi, Kenichi
Parole chiave
  • disordered systems
  • matching
  • optimization
  • replica method
  • statistical physics
  • stochastic processes
Data inizio appello
10/02/2015
Consultabilità
Non consultabile
Data di rilascio
10/02/2085
Riassunto
In the present thesis we discuss the so-called Euclidean Matching Problem. We overview the main results obtained in the last fifty years on Random Optimization Problems, stressing the important contributions given by Statistical Physics and describing the most powerful tools used, prevalently borrowed from Spin Glass Theory. In the spirit of the classic results, we studied the Euclidean Matching Problem following very different approaches, showing its connections with the Theory of Stochastic Processes, Measure Theory and the Theory of Disordered Systems. We developed new methods to analyse this combinatorial problem inspired by its continuum versions as transport problem between measures and treating Euclidean correlations as a perturbation to the purely random case.
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