D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Metal?insulator transition in a weakly interacting many-electron system with localized single-particle states, Annals of Physics, vol.321, issue.5, p.1126, 2006.
DOI : 10.1016/j.aop.2005.11.014

URL : https://hal.archives-ouvertes.fr/hal-00371119

E. Altman and R. Vosk, Universal Dynamics and Renormalization in Many-Body-Localized Systems, Annual Review of Condensed Matter Physics, vol.6, issue.1, p.383, 2015.
DOI : 10.1146/annurev-conmatphys-031214-014701

URL : http://arxiv.org/abs/1408.2834

R. Nandkishore and D. A. Huse, Many-Body Localization and Thermalization in Quantum Statistical Mechanics, Annual Review of Condensed Matter Physics, vol.6, issue.1, p.15, 2015.
DOI : 10.1146/annurev-conmatphys-031214-014726

URL : http://arxiv.org/abs/1404.0686

K. Agarwal, S. Gopalakrishnan, M. Knap, M. Müller, and E. Demler, Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition, Physical Review Letters, vol.114, issue.16, p.160401, 2015.
DOI : 10.1016/j.physa.2013.11.023

URL : http://arxiv.org/abs/1408.3413

D. J. Luitz, N. Laflorencie, and F. Alet, Extended slow dynamical regime close to the many-body localization transition, Physical Review B, vol.93, issue.6, p.60201, 2016.
DOI : 10.1103/PhysRevB.92.195153

URL : https://hal.archives-ouvertes.fr/hal-01328914

E. J. Torres-herrera and L. F. Santos, Dynamics at the many-body localization transition, Physical Review B, vol.92, issue.1, p.14208, 2015.
DOI : 10.1103/PhysRevE.54.3221

URL : http://arxiv.org/abs/1501.05662

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Luschen, M. H. Fischer et al., Observation of many-body localization of interacting fermions in a quasirandom optical lattice, Science, vol.326, issue.4, p.842, 2015.
DOI : 10.1016/j.aop.2010.09.012

S. Gopalakrishnan, K. Agarwal, E. A. Demler, D. A. Huse, and M. Knap, Griffiths effects and slow dynamics in nearly many-body localized systems, Physical Review B, vol.93, issue.13, p.134206, 2016.
DOI : 10.1103/PhysRevX.2.041020

URL : http://arxiv.org/abs/1511.06389

B. L. Altshuler, Y. Gefen, A. Kamenev, and L. S. Levitov, Quasiparticle Lifetime in a Finite System: A Nonperturbative Approach, Physical Review Letters, vol.8, issue.14, p.2803, 1997.
DOI : 10.1051/jp1:1995169

A. De-luca, B. L. Altshuler, V. E. Kravtsov, and A. Scardicchio, Anderson Localization on the Bethe Lattice: Nonergodicity of Extended States, Physical Review Letters, vol.95, issue.4, p.46806, 2014.
DOI : 10.1103/PhysRevB.56.13393

B. L. Altshuler, E. Cuevas, L. B. Ioffe, and V. E. Kravtsov, Nonergodic Phases in Strongly Disordered Random Regular Graphs, Physical Review Letters, vol.11, issue.15, p.156601, 2016.
DOI : 10.1007/978-1-4757-2063-1

URL : https://hal.archives-ouvertes.fr/hal-01400928

K. S. Tikhonov, A. D. Mirlin, and M. A. Skvortsov, Anderson localization and ergodicity on random regular graphs, Physical Review B, vol.66, issue.22, p.220203, 2016.
DOI : 10.1103/PhysRevLett.117.156601

E. Tarquini, G. Biroli, and M. Tarzia, Level Statistics and Localization Transitions of L?vy Matrices, Physical Review Letters, vol.2010, issue.1, p.10601, 2016.
DOI : 10.1103/PhysRevB.75.155111

URL : http://arxiv.org/abs/1507.00296

V. E. Kravtsov, I. M. Khaymovich, E. Cuevas, and M. Amini, A random matrix model with localization and ergodic transitions, New Journal of Physics, vol.17, issue.12, p.122002, 2015.
DOI : 10.1088/1367-2630/17/12/122002

URL : http://doi.org/10.1088/1367-2630/17/12/122002

D. Facoetti, P. Vivo, and G. Biroli, From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective, EPL (Europhysics Letters), vol.115, issue.4, p.47003, 2016.
DOI : 10.1209/0295-5075/115/47003

URL : http://arxiv.org/abs/1607.05942

D. E. Logan and P. G. Wolynes, Dephasing and Anderson localization in topologically disordered systems, Proc. Nat. Acad. Sci. 95, pp.4135-4994, 1987.
DOI : 10.1002/9780470142752.ch5

N. C. Wormald, Models of random-regular graphs, in Surveys in, p.239, 1999.

J. T. Chalker and G. J. , Scaling, Diffusion, and the Integer Quantized Hall Effect, Physical Review Letters, vol.16, issue.5, p.593, 1988.
DOI : 10.1088/0022-3719/16/6/007

E. Cuevas and V. E. Kravtsov, Two-eigenfunction correlation in a multifractal metal and insulator, Physical Review B, vol.38, issue.23, p.235119, 2007.
DOI : 10.1103/PhysRevB.22.3598

URL : http://arxiv.org/abs/0707.4585

D. J. Luitz and Y. Lev, Anomalous Thermalization in Ergodic Systems, Physical Review Letters, vol.117, issue.17, p.170404, 2016.
DOI : 10.1145/1089014.1089019

URL : http://arxiv.org/abs/1607.01012

W. De-roeck and J. Z. Imbrie, SUPPLEMENTAL MATERIAL In this supplemental materials we illustrate and discuss in more detail the finite-size effects observed on the time-dependence of dynamical observables at small sizes and very large times-scales