Giulio Biroli et al J. Stat. Mech. (2007) P07019 doi:10.1088/1742-5468/2007/07/P07019
Extreme value problems in random matrix theory and other disordered systems
FREE ARTICLE Focus on Dynamics of Non-Equilibrium SystemsGiulio Biroli1,2, Jean-Philippe Bouchaud2,3 and Marc Potters2
Show affiliationsPart of Focus on Dynamics of Non-Equilibrium Systems
We review some applications of central limit theorems and extreme values statistics in the context of disordered systems. We discuss several problems, in particular concerning random matrix theory and the generalization of the Tracy–Widom distribution when the disorder has 'fat tails'. We underline the relevance of power-law tails for directed polymers and mean-field spin glasses and we point out various open problems and conjectures on these matters. We find that, in many instances, the assumption of Gaussian disorder cannot be taken for granted.
- Keywords
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E-print Number: cond-mat/0702244
Cited: by |
Refers: to
- PACS
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75.50.Lk Spin glasses and other random magnets
05.40.Fb Random walks and Levy flights
- MSC
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15A18 Eigenvalues, singular values, and eigenvectors
60J65 Brownian motion (See also 58J65)
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
82C44 Dynamics of disordered systems (random Ising systems, etc.)
- Subjects
- Dates
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Issue 07 (July 2007)
Received 12 February 2007, accepted for publication 6 March 2007
Published 24 July 2007
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Extreme value problems in random matrix theory and other disordered systems
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