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https://hdl.handle.net/2445/223117
Title: | Spectral density of Wishart matrices and the replica method |
Author: | Martínez Ortega, Pol |
Director/Tutor: | Palassini, Matteo |
Keywords: | Sistemes complexos Matrius aleatòries Treballs de fi de grau Complex systems Random matrices Bachelor's theses |
Issue Date: | Jun-2025 |
Abstract: | Random matrix theory provides a powerful framework for understanding universal features of complex systems, especially in the large-size limit. In this work, we study the spectral density of Wishart-Laguerre random matrices using the Edwards-Jones formula. We reinterpret the averaged quantity in the Edwards-Jones formula as the partition function of a disordered system and apply tools from statistical physics. Our results illustrate how techniques from statistical physics of disordered systems naturally extend to random matrix theory, offering physical insight and analytical methods for exploring spectral properties in complex systems |
Note: | Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2025, Tutor: Matteo Palassini |
URI: | https://hdl.handle.net/2445/223117 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Física |
Files in This Item:
File | Description | Size | Format | |
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MARTÍNEZ ORTEGA POL-R.pdf | 307.65 kB | Adobe PDF | View/Open |
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