On the high-density expansion for Euclidean random matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown t...

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Autores principales: Grigera, Tomás Sebastián, Martin-Mayor, Victor, Parisi, Giorgio, Urbani, Pierfrancesco, Verrocchio, Paolo
Formato: Articulo
Lenguaje:Inglés
Publicado: 2011
Materias:
Ciencias Exactas
Física
random matrix theory and extensions
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/132236
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-132236
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Física
random matrix theory and extensions
spellingShingle Ciencias Exactas
Física
random matrix theory and extensions
Grigera, Tomás Sebastián
Martin-Mayor, Victor
Parisi, Giorgio
Urbani, Pierfrancesco
Verrocchio, Paolo
On the high-density expansion for Euclidean random matrices
topic_facet Ciencias Exactas
Física
random matrix theory and extensions
description Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.
format Articulo
Articulo
author Grigera, Tomás Sebastián
Martin-Mayor, Victor
Parisi, Giorgio
Urbani, Pierfrancesco
Verrocchio, Paolo
author_facet Grigera, Tomás Sebastián
Martin-Mayor, Victor
Parisi, Giorgio
Urbani, Pierfrancesco
Verrocchio, Paolo
author_sort Grigera, Tomás Sebastián
title On the high-density expansion for Euclidean random matrices
title_short On the high-density expansion for Euclidean random matrices
title_full On the high-density expansion for Euclidean random matrices
title_fullStr On the high-density expansion for Euclidean random matrices
title_full_unstemmed On the high-density expansion for Euclidean random matrices
title_sort on the high-density expansion for euclidean random matrices
publishDate 2011
url http://sedici.unlp.edu.ar/handle/10915/132236
work_keys_str_mv AT grigeratomassebastian onthehighdensityexpansionforeuclideanrandommatrices
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AT parisigiorgio onthehighdensityexpansionforeuclideanrandommatrices
AT urbanipierfrancesco onthehighdensityexpansionforeuclideanrandommatrices
AT verrocchiopaolo onthehighdensityexpansionforeuclideanrandommatrices
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