E. Witten, Quarks, atoms, and the 1/N expansion, Physics Today, vol.33, issue.7, p.38, 1980.
DOI : 10.1063/1.2914163

D. Wyler, N. Rivier, and H. Frisch, Hard-sphere fluid in infinite dimensions, Physical Review A, vol.36, issue.5, pp.2422-2431, 1987.
DOI : 10.1103/PhysRevA.36.2422

H. Frisch and J. Percus, High dimensionality as an organizing device for classical fluids, Physical Review E, vol.60, issue.3, pp.2942-2948, 1999.
DOI : 10.1103/PhysRevE.60.2942

A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Reviews of Modern Physics, vol.68, issue.1, p.13, 1996.
DOI : 10.1103/RevModPhys.68.13

A. Svidzinsky, M. Scully, and D. Herschbach, Bohr???s molecular model, a century later, Physics Today, vol.67, issue.1, p.33, 2014.
DOI : 10.1063/PT.3.2243

J. Drouffe, G. Parisi, and N. Sourlas, Strong coupling phase in lattice gauge theories at large dimension, Nuclear Physics B, vol.161, issue.2-3, pp.397-416, 1979.
DOI : 10.1016/0550-3213(79)90220-7
URL : http://doi.org/10.1016/0550-3213(79)90220-7

T. Kirkpatrick and P. Wolynes, Connections between some kinetic and equilibrium theories of the glass transition, Physical Review A, vol.35, issue.7, pp.3072-3080, 1987.
DOI : 10.1103/PhysRevA.35.3072

T. Kirkpatrick and P. Wolynes, Stable and metastable states in mean-field Potts and structural glasses, Physical Review B, vol.36, issue.16, pp.8552-8564, 1987.
DOI : 10.1103/PhysRevB.36.8552

T. Kirkpatrick and D. Thirumalai, -Spin???Interaction Spin-Glass Model, Physical Review Letters, vol.58, issue.20, pp.2091-2094, 1987.
DOI : 10.1103/PhysRevLett.58.2091
URL : https://hal.archives-ouvertes.fr/jpa-00210072

T. Kirkpatrick and D. Thirumalai, -spin-interaction spin-glass models: Connections with the structural glass problem, Physical Review B, vol.36, issue.10, pp.5388-5397, 1987.
DOI : 10.1103/PhysRevB.36.5388
URL : https://hal.archives-ouvertes.fr/jpa-00210072

T. Kirkpatrick and D. Thirumalai, Comparison between dynamical theories and metastable states in regular and glassy mean-field spin models with underlying first-order-like phase transitions, Physical Review A, vol.37, issue.11, pp.4439-4448, 1988.
DOI : 10.1103/PhysRevA.37.4439

G. Parisi and F. Zamponi, Mean-field theory of hard sphere glasses and jamming, Reviews of Modern Physics, vol.82, issue.1, pp.789-845, 2010.
DOI : 10.1103/RevModPhys.82.789

W. Kauzmann, The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures., Chemical Reviews, vol.43, issue.2, pp.219-256, 1948.
DOI : 10.1021/cr60135a002

J. Bouchaud and G. Biroli, On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses, The Journal of Chemical Physics, vol.121, issue.15, p.7347, 2004.
DOI : 10.1063/1.1796231

J. Conway and N. Sloane, Sphere packings, lattices and groups, of A Series of Comprehensive Mathematics, 1999.

M. Skoge, A. Donev, F. Stillinger, and S. Torquato, Packing hyperspheres in high-dimensional Euclidean spaces, Physical Review E, vol.74, issue.4, p.41127, 2006.
DOI : 10.1103/PhysRevE.74.041127
URL : http://arxiv.org/abs/cond-mat/0608362

J. Eaves and D. Reichman, Spatial dimension and the dynamics of supercooled liquids, Proceedings of the National Academy of Sciences, vol.106, issue.36, p.15171, 2009.
DOI : 10.1073/pnas.0902888106

J. Van-meel, D. Frenkel, and P. Charbonneau, Geometrical frustration: A study of four-dimensional hard spheres, Physical Review E, vol.79, issue.3, p.30201, 2009.
DOI : 10.1103/PhysRevE.79.030201

J. Van-meel, B. Charbonneau, A. Fortini, and P. Charbonneau, Hard-sphere crystallization gets rarer with increasing dimension, Physical Review E, vol.80, issue.6, p.61110, 2009.
DOI : 10.1103/PhysRevE.80.061110

P. Charbonneau, A. Ikeda, J. Van-meel, and K. Miyazaki, Numerical and theoretical study of a monodisperse hard-sphere glass former, Physical Review E, vol.81, issue.4, p.40501, 2010.
DOI : 10.1103/PhysRevE.81.040501

P. Charbonneau, A. Ikeda, G. Parisi, and F. Zamponi, Glass Transition and Random Close Packing above Three Dimensions, Physical Review Letters, vol.107, issue.18, p.185702, 2011.
DOI : 10.1103/PhysRevLett.107.185702
URL : http://arxiv.org/abs/1107.4666

B. Charbonneau, P. Charbonneau, and G. Tarjus, Geometrical Frustration and Static Correlations in a Simple Glass Former, Physical Review Letters, vol.108, issue.3, p.35701, 2012.
DOI : 10.1103/PhysRevLett.108.035701

K. Zhang, W. Smith, M. Wang, Y. Liu, and J. Schroers, Connection between the packing efficiency of binary hard spheres and the glass-forming ability of bulk metallic glasses, Physical Review E, vol.90, issue.3, p.32311, 2014.
DOI : 10.1103/PhysRevE.90.032311

T. Maimbourg, J. Kurchan, and F. Zamponi, Solution of the Dynamics of Liquids in the Large-Dimensional Limit, Physical Review Letters, vol.116, issue.1, p.15902, 2016.
DOI : 10.1103/PhysRevLett.116.015902

L. Cugliandolo and J. Kurchan, Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model, Physical Review Letters, vol.71, issue.1, pp.173-176, 1993.
DOI : 10.1103/PhysRevLett.71.173

L. Cugliandolo, Dynamics of glassy systems. In Slow Relaxations and nonequilibrium dynamics in condensed matter, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00102091

J. Bouchaud, L. Cugliandolo, J. Kurchan, and M. Mézard, OUT OF EQUILIBRIUM DYNAMICS IN SPIN-GLASSES AND OTHER GLASSY SYSTEMS, Spin Glasses And Random Fields, 1997.
DOI : 10.1142/9789812819437_0006

W. Götze, Complex dynamics of glass-forming liquids: A mode-coupling theory, 2008.
DOI : 10.1093/acprof:oso/9780199235346.001.0001

P. Charbonneau, A. Ikeda, G. Parisi, and F. Zamponi, Dimensional study of the caging order parameter at the glass transition, Proceedings of the National Academy of Sciences, vol.109, issue.35, pp.13939-13943, 2012.
DOI : 10.1073/pnas.1211825109

P. Charbonneau, J. Y. Parisi, G. Zamponi, and F. , Hopping and the Stokes???Einstein relation breakdown in simple glass formers, Proceedings of the National Academy of Sciences, vol.111, issue.42, pp.15025-15030, 2014.
DOI : 10.1073/pnas.1417182111

B. Charbonneau, P. Charbonneau, J. Y. Parisi, G. Zamponi, and F. , Dimensional dependence of the Stokes???Einstein relation and its violation, The Journal of Chemical Physics, vol.139, issue.16, p.164502, 2013.
DOI : 10.1063/1.4825177

J. Kurchan, G. Parisi, and F. Zamponi, Exact theory of dense amorphous hard spheres in high dimension I. The free energy, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.10, p.10012, 2012.
DOI : 10.1088/1742-5468/2012/10/P10012

J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Exact Theory of Dense Amorphous Hard Spheres in High Dimension. II. The High Density Regime and the Gardner Transition, The Journal of Physical Chemistry B, vol.117, issue.42, pp.12979-12994, 2013.
DOI : 10.1021/jp402235d
URL : https://hal.archives-ouvertes.fr/cea-01464503

S. Franz and G. Parisi, On non-linear susceptibility in supercooled liquids, Journal of Physics: Condensed Matter, vol.12, issue.29, p.6335, 2000.
DOI : 10.1088/0953-8984/12/29/305

L. Berthier, G. Biroli, J. Bouchaud, W. Kob, K. Miyazaki et al., Spontaneous and induced dynamic fluctuations in glass formers. I. General results and dependence on ensemble and dynamics, The Journal of Chemical Physics, vol.126, issue.18, p.184503, 2007.
DOI : 10.1063/1.2721554
URL : http://arxiv.org/abs/cond-mat/0609656

L. Berthier, G. Biroli, J. Bouchaud, W. Kob, K. Miyazaki et al., Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations, The Journal of Chemical Physics, vol.126, issue.18, p.184504, 2007.
DOI : 10.1063/1.2721555

L. Berthier, G. Biroli, J. Bouchaud, L. Cipelletti, E. Masri et al., Direct Experimental Evidence of a Growing Length Scale Accompanying the Glass Transition, Science, vol.310, issue.5755, pp.1797-1800, 2005.
DOI : 10.1126/science.1120714
URL : https://hal.archives-ouvertes.fr/cea-01395308

L. Berthier, G. Biroli, J. Bouchaud, L. Cipelletti, and W. Van-saarloos, Dynamical heterogeneities and glasses, 2011.

S. Nandi, G. Biroli, and G. Tarjus, Spinodals with Disorder: From Avalanches in Random Magnets to Glassy Dynamics, Physical Review Letters, vol.116, issue.14, p.145701, 2016.
DOI : 10.1103/PhysRevLett.116.145701
URL : https://hal.archives-ouvertes.fr/cea-01188243

A. Ikeda and K. Miyazaki, Mode-Coupling Theory as a Mean-Field Description of the Glass Transition, Physical Review Letters, vol.104, issue.25, p.255704, 2010.
DOI : 10.1103/PhysRevLett.104.255704

B. Schmid and R. Schilling, Glass transition of hard spheres in high dimensions, Physical Review E, vol.81, issue.4, p.41502, 2010.
DOI : 10.1103/PhysRevE.81.041502

M. Mangeat and F. Zamponi, Quantitative approximation schemes for glasses, Physical Review E, vol.93, issue.1, p.12609, 2016.
DOI : 10.1103/PhysRevE.93.012609
URL : http://arxiv.org/abs/1510.03808

D. Coslovich, A. Ikeda, and K. Miyazaki, Mean-field dynamic criticality and geometric transition in the Gaussian core model, Physical Review E, vol.93, issue.4, p.42602, 2016.
DOI : 10.1103/PhysRevE.93.042602
URL : https://hal.archives-ouvertes.fr/hal-01310191

M. Mézard, G. Parisi, M. Virasoro, A. Bray, and M. Moore, Spin glass theory and beyond. Singapore: World Scientific 58, J. Phys. C, vol.13, p.469, 1980.

G. Biroli and J. Kurchan, Metastable states in glassy systems, Physical Review E, vol.64, issue.1, p.16101, 2001.
DOI : 10.1103/PhysRevE.64.016101
URL : http://arxiv.org/abs/cond-mat/0005499

A. Barrat, R. Burioni, and M. Mézard, Dynamics within metastable states in a mean-field spin glass, Journal of Physics A: Mathematical and General, vol.29, issue.5, p.81, 1996.
DOI : 10.1088/0305-4470/29/5/001

S. Franz and G. Parisi, Quasi-equilibrium in glassy dynamics: an algebraic view, Journal of Statistical Mechanics: Theory and Experiment, vol.2013, issue.02, p.2003, 2013.
DOI : 10.1088/1742-5468/2013/02/P02003
URL : https://hal.archives-ouvertes.fr/hal-00807927

J. Kurchan and F. Ritort, Rheology, and how to stop aging In Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales, Europhys. Lett, vol.51, p.147, 2000.

S. Franz and M. Virasoro, Quasi-equilibrium interpretation of ageing dynamics, Journal of Physics A: Mathematical and General, vol.33, issue.5, p.891, 2000.
DOI : 10.1088/0305-4470/33/5/306

F. Caltagirone, U. Ferrari, L. Leuzzi, G. Parisi, F. Ricci-tersenghi et al., Critical Slowing Down Exponents of Mode Coupling Theory, Physical Review Letters, vol.108, issue.8, p.85702, 2012.
DOI : 10.1103/PhysRevLett.108.085702

G. Parisi and T. Rizzo, Critical dynamics in glassy systems, Physical Review E, vol.87, issue.1, p.12101, 2013.
DOI : 10.1103/PhysRevE.87.012101

A. Barrat, S. Franz, and G. Parisi, Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses, Journal of Physics A: Mathematical and General, vol.30, issue.16, pp.5593-5612, 1997.
DOI : 10.1088/0305-4470/30/16/006

C. Rainone, P. Urbani, H. Yoshino, and F. Zamponi, Following the Evolution of Hard Sphere Glasses in Infinite Dimensions under External Perturbations: Compression and Shear Strain, Physical Review Letters, vol.114, issue.1, p.15701, 2015.
DOI : 10.1103/PhysRevLett.114.015701

C. Rainone and P. Urbani, Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution, Journal of Statistical Mechanics: Theory and Experiment, vol.2016, issue.5, p.53302, 2016.
DOI : 10.1088/1742-5468/2016/05/053302
URL : https://hal.archives-ouvertes.fr/cea-01463152

S. Franz, G. Parisi, P. Urbani, and F. Zamponi, Universal spectrum of normal modes in low-temperature glasses, Proceedings of the National Academy of Sciences, vol.112, issue.47, pp.14539-14544, 2015.
DOI : 10.1073/pnas.1511134112
URL : https://hal.archives-ouvertes.fr/hal-01237684

P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Exact theory of dense amorphous hard spheres in high dimension. III. The full replica symmetry breaking solution, Journal of Statistical Mechanics: Theory and Experiment, vol.2014, issue.10, p.10009, 2014.
DOI : 10.1088/1742-5468/2014/10/P10009
URL : https://hal.archives-ouvertes.fr/cea-01464503

E. Gardner, Spin glasses with p-spin interactions, Nuclear Physics B, vol.257, pp.747-765, 1985.
DOI : 10.1016/0550-3213(85)90374-8
URL : http://doi.org/10.1016/0550-3213(85)90374-8

D. Gross, I. Kanter, and H. Sompolinsky, Mean-field theory of the Potts glass, Physical Review Letters, vol.55, issue.3, p.304, 1985.
DOI : 10.1103/PhysRevLett.55.304

P. Charbonneau, J. Y. Parisi, G. Rainone, C. Seoane, B. Zamponi et al., Numerical detection of the Gardner transition in a mean-field glass former, Physical Review E, vol.92, issue.1, p.12316, 2015.
DOI : 10.1103/PhysRevE.92.012316

J. Dyre, : The glass transition and elastic models of glass-forming liquids, Reviews of Modern Physics, vol.78, issue.3, p.953, 2006.
DOI : 10.1103/RevModPhys.78.953

P. Urbani and G. Biroli, Gardner transition in finite dimensions, Physical Review B, vol.91, issue.10, p.100202, 2015.
DOI : 10.1103/PhysRevB.91.100202

O. Hern, C. Langer, S. Liu, A. Nagel, and S. , Random Packings of Frictionless Particles, Physical Review Letters, vol.88, issue.7, p.75507, 2002.
DOI : 10.1103/PhysRevLett.88.075507

S. Torquato and F. Stillinger, Jammed hard-particle packings: From Kepler to Bernal and beyond, Reviews of Modern Physics, vol.82, issue.3, pp.2633-2672, 2010.
DOI : 10.1103/RevModPhys.82.2633

M. Müller and M. Wyart, Marginal Stability in Structural, Spin, and Electron Glasses, Annual Review of Condensed Matter Physics, vol.6, issue.1, pp.177-200, 2015.
DOI : 10.1146/annurev-conmatphys-031214-014614

L. Bo, M. R. Song, C. Makse, and H. , Cavity method for force transmission in jammed disordered packings of hard particles, Soft Matter, vol.10, issue.37, pp.7379-7392, 2014.
DOI : 10.1039/C4SM00667D

L. Silbert, A. Liu, and S. Nagel, Vibrations and Diverging Length Scales Near the Unjamming Transition, Physical Review Letters, vol.95, issue.9, p.98301, 2005.
DOI : 10.1103/PhysRevLett.95.098301
URL : http://arxiv.org/abs/cond-mat/0501616

M. Wyart, S. Nagel, and T. Witten, Geometric origin of excess low-frequency vibrational modes in weakly connected amorphous solids, Europhysics Letters (EPL), vol.72, issue.3, pp.486-492, 2005.
DOI : 10.1209/epl/i2005-10245-5

M. Wyart, L. Silbert, S. Nagel, and T. Witten, Effects of compression on the vibrational modes of marginally jammed solids, Physical Review E, vol.72, issue.5, p.51306, 2005.
DOI : 10.1103/PhysRevE.72.051306

E. Degiuli, A. Laversanne-finot, G. Düring, E. Lerner, and M. Wyart, Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids, Soft Matter, vol.104, issue.3, pp.5628-5644, 2014.
DOI : 10.1039/C4SM00561A

N. Xu, V. Vitelli, A. Liu, and S. Nagel, Anharmonic and quasi-localized vibrations in jammed solids???Modes for mechanical failure, EPL (Europhysics Letters), vol.90, issue.5, p.56001, 2010.
DOI : 10.1209/0295-5075/90/56001

M. Wyart, Marginal Stability Constrains Force and Pair Distributions at Random Close Packing, Physical Review Letters, vol.109, issue.12, p.125502, 2012.
DOI : 10.1103/PhysRevLett.109.125502

P. Charbonneau, E. Corwin, G. Parisi, and F. Zamponi, Jamming Criticality Revealed by Removing Localized Buckling Excitations, Physical Review Letters, vol.114, issue.12, p.125504, 2015.
DOI : 10.1103/PhysRevLett.114.125504
URL : http://arxiv.org/abs/1411.3975

E. Lerner, G. Düring, and M. Wyart, Low-energy non-linear excitations in sphere packings, Soft Matter, vol.184, issue.3, pp.8252-8263, 2013.
DOI : 10.1039/c3sm50515d

P. Charbonneau, E. Corwin, G. Parisi, and F. Zamponi, Universal Microstructure and Mechanical Stability of Jammed Packings, Physical Review Letters, vol.109, issue.20, p.205501, 2012.
DOI : 10.1103/PhysRevLett.109.205501

P. Chaudhuri, L. Berthier, and S. Sastry, Jamming Transitions in Amorphous Packings of Frictionless Spheres Occur over a Continuous Range of Volume Fractions, Physical Review Letters, vol.104, issue.16, p.165701, 2010.
DOI : 10.1103/PhysRevLett.104.165701
URL : https://hal.archives-ouvertes.fr/hal-00514499

M. Ozawa, T. Kuroiwa, A. Ikeda, and K. Miyazaki, Jamming Transition and Inherent Structures of Hard Spheres and Disks, Physical Review Letters, vol.109, issue.20, p.205701, 2012.
DOI : 10.1103/PhysRevLett.109.205701

C. Goodrich, A. Liu, and S. Nagel, Finite-Size Scaling at the Jamming Transition, Physical Review Letters, vol.109, issue.9, p.95704, 2012.
DOI : 10.1103/PhysRevLett.109.095704

C. Brito and M. Wyart, Geometric interpretation of previtrification in hard sphere liquids, The Journal of Chemical Physics, vol.131, issue.2, p.24504, 2009.
DOI : 10.1063/1.3157261

F. Stillinger and T. Weber, Hidden structure in liquids, Physical Review A, vol.25, issue.2, pp.978-989, 1982.
DOI : 10.1103/PhysRevA.25.978

F. Sciortino, W. Kob, and P. Tartaglia, Inherent Structure Entropy of Supercooled Liquids, Physical Review Letters, vol.83, issue.16, pp.3214-3217, 1999.
DOI : 10.1103/PhysRevLett.83.3214

G. Biroli and R. Monasson, From inherent structures to pure states: Some simple remarks and examples, Europhysics Letters (EPL), vol.50, issue.2, pp.155-161, 2000.
DOI : 10.1209/epl/i2000-00248-2
URL : http://arxiv.org/abs/cond-mat/9912061

L. Berthier, H. Jacquin, and F. Zamponi, Microscopic theory of the jamming transition of harmonic spheres, Physical Review E, vol.84, issue.5, p.51103, 2011.
DOI : 10.1103/PhysRevE.84.051103
URL : https://hal.archives-ouvertes.fr/hal-00643045

R. Monasson, Structural Glass Transition and the Entropy of the Metastable States, Physical Review Letters, vol.75, issue.15, pp.2847-2850, 1995.
DOI : 10.1103/PhysRevLett.75.2847

T. Rizzo, Replica-symmetry-breaking transitions and off-equilibrium dynamics, Physical Review E, vol.88, issue.3, p.32135, 2013.
DOI : 10.1103/PhysRevE.88.032135
URL : http://arxiv.org/abs/1305.2070

L. Cugliandolo and J. Kurchan, On the out-of-equilibrium relaxation of the Sherrington-Kirkpatrick model, Journal of Physics A: Mathematical and General, vol.27, issue.17, p.5749, 1994.
DOI : 10.1088/0305-4470/27/17/011

M. Van-hecke, Jamming of soft particles: geometry, mechanics, scaling and isostaticity, Journal of Physics: Condensed Matter, vol.22, issue.3, p.33101, 2010.
DOI : 10.1088/0953-8984/22/3/033101

B. Lubachevsky and F. Stillinger, Geometric properties of random disk packings, Journal of Statistical Physics, vol.58, issue.1, pp.561-583, 1990.
DOI : 10.1007/BF01025983

E. Lerner, G. Düring, and M. Wyart, Simulations of driven overdamped frictionless hard spheres, Computer Physics Communications, vol.184, issue.3, pp.628-637, 2013.
DOI : 10.1016/j.cpc.2012.10.020

S. Torquato and Y. Jiao, Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming, Physical Review E, vol.82, issue.6, p.61302, 2010.
DOI : 10.1103/PhysRevE.82.061302

A. Hopkins, F. Stillinger, and S. Torquato, Disordered strictly jammed binary sphere packings attain an anomalously large range of densities, Physical Review E, vol.88, issue.2, p.22205, 2013.
DOI : 10.1103/PhysRevE.88.022205

N. Xu, D. Frenkel, and A. Liu, Direct Determination of the Size of Basins of Attraction of Jammed Solids, Physical Review Letters, vol.106, issue.24, p.245502, 2011.
DOI : 10.1103/PhysRevLett.106.245502

D. Asenjo, F. Paillusson, and D. Frenkel, Numerical Calculation of Granular Entropy, Physical Review Letters, vol.112, issue.9, pp.98002-122208001, 2014.
DOI : 10.1103/PhysRevLett.112.098002