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Cleaning large correlation matrices: tools from random matrix theory

Joël Bun 1, 2 Jean-Philippe Bouchaud 2 Marc Potters 2 Physics Reports, Elsevier, 2017, 666, pp.1 This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on

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Asymptotically optimal control for a simplest distributed system

Alexander Ovseevich 1 Aleksey Fedorov 2 Доклады Академии Наук / Doklady Mathematics, MAIK Nauka/Interperiodica, 2017, 95 (2), pp.194 – 197 We study the problem of the minimum-time damping of a closed string under a bounded load, applied at a single fixed point. A constructive feedback control law is designed, which allows bringing the system to

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Archive ouverte HAL – Statistics of fermions in a d-dimensional box near a hard wall

Bertrand Lacroix-A-Chez-Toine 1 Pierre Le Doussal 2 Satya Majumdar 1 Grégory Schehr 1 EPL, 2017, 120 (1), pp.10006. 〈10.1209/0295-5075/120/10006〉 We study N noninteracting fermions in a domain bounded by a hard-wall potential in dimensions. We show that for large N, the correlations at the edge of the Fermi gas (near the wall) at zero temperature

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Archive ouverte HAL – Statistics of fermions in a $d$-dimensional box near a hard wall

Bertrand Lacroix-A-Chez-Toine 1 Pierre Le Doussal 2 Satya N. Majumdar 1 Gregory Schehr 1 EPL – Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017 We study $N$ noninteracting fermions in a domain bounded by a hard wall potential in $d \geq 1$ dimensions. We show that for large $N$, the correlations at

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Archive ouverte HAL – Quantum quenches with random matrix Hamiltonians and disordered potentials

Fabian Kolley 1 Oriol Bohigas 2 Boris V. Fine 1, 3 Annalen der Physik, 2017 We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists

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Archive ouverte HAL – Non-equilibrium fluctuations of a semi-flexible filament driven by active cross-linkers

Ines Weber 1, 2 Cecile Appert-Rolland 2 Gregory Schehr 3 Ludger Santen 1 EPL – Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017 The cytoskeleton is an inhomogeneous network of semi-flexible filaments, which are involved in a wide variety of active biological processes. Although the cytoskeletal filaments can be very stiff and

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