P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the Fast Scrambling Conjecture, JHEP 04 (2013) 022 [arXiv:1111.6580] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
A. Kitaev, Hidden correlations in the hawking radiation and thermal noise, talks given at The Fundamental Physics Prize Symposium, 10 November 2014, and at The KITP, 12 February 2015.
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography, talks given at The KITP, 7 April 2015 and 27 May 2015.
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
J.S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [arXiv:1611.04650] [INSPIRE].
E.P. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. Math. 62 (1955) 548.
F.J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3 (1962) 140 [INSPIRE].
O. Bohigas, M.J. Giannoni and C. Schmit, Characterization of chaotic quantum spectra and universality of level fluctuation laws, Phys. Rev. Lett. 52 (1984) 1 [INSPIRE].
P. Hosur, X.-L. Qi, D.A. Roberts and B. Yoshida, Chaos in quantum channels, JHEP 02 (2016) 004 [arXiv:1511.04021] [INSPIRE].
D.A. Roberts and B. Yoshida, Chaos and complexity by design, JHEP 04 (2017) 121 [arXiv:1610.04903] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, On information loss in AdS
, JHEP 05 (2016) 109 [arXiv:1603.08925] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles, JHEP 04 (2017) 072 [arXiv:1609.07153] [INSPIRE].
E. Dyer and G. Gur-Ari, 2D CFT Partition Functions at Late Times, JHEP 08 (2017) 075 [arXiv:1611.04592] [INSPIRE].
V. Balasubramanian, B. Craps, B. Czech and G. Sárosi, Echoes of chaos from string theory black holes, JHEP 03 (2017) 154 [arXiv:1612.04334] [INSPIRE].
Y.-Z. You, A.W.W. Ludwig and C. Xu, Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States, Phys. Rev. B 95 (2017) 115150 [arXiv:1602.06964] [INSPIRE].
A.M. García-García and J.J.M. Verbaarschot, Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 126010 [arXiv:1610.03816] [INSPIRE].
M. Mehta, Random Matrices, Pure and Applied Mathematics, Elsevier Science (2004).
T. Tao, Topics in Random Matrix Theory, Graduate studies in mathematics, American Mathematical Society (2012).
T. Guhr, A. Müller-Groeling and H.A. Weidenmuller, Random matrix theories in quantum physics: Common concepts, Phys. Rept. 299 (1998) 189 [cond-mat/9707301] [INSPIRE].
A.R. Brown and L. Susskind, The Second Law of Quantum Complexity, arXiv:1701.01107 [INSPIRE].
A. del Campo, J. Molina-Vilaplana and J. Sonner, Scrambling the spectral form factor: unitarity constraints and exact results, Phys. Rev. D 95 (2017) 126008 [arXiv:1702.04350] [INSPIRE].
E. Brézin and S. Hikami, Spectral form factor in a random matrix theory, Phys. Rev. E 55 (1997) 4067 [cond-mat/9608116].
L. Erdős and D. Schröder, Phase Transition in the Density of States of Quantum Spin Glasses, Math. Phys. Anal. Geom. 17 (2014) 9164 [arXiv:1407.1552].
J.S. Cotler, G.R. Penington and D.H. Ranard, Locality from the Spectrum, arXiv:1702.06142 [INSPIRE].
A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical Method in the Theory of Superconductivity, JETP 28 (1969) 1200.
D. Bagrets, A. Altland and A. Kamenev, Power-law out of time order correlation functions in the SYK model, Nucl. Phys. B 921 (2017) 727 [arXiv:1702.08902] [INSPIRE].
F.G.S.L. Brandão, P. Ćwiklinski, M. Horodecki, P. Horodecki, J.K. Korbicz and M. Mozrzymas, Convergence to equilibrium under a random hamiltonian, Phys. Rev. E 86 (2012) 031101 [arXiv:1108.2985].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
Z.-W. Liu, S. Lloyd, E.Y. Zhu and H. Zhu, Entropic scrambling complexities, arXiv:1703.08104 [INSPIRE].
C. Dankert, R. Cleve, J. Emerson and E. Livine, Exact and approximate unitary 2-designs and their application to fidelity estimation, Phys. Rev. A 80 (2009) 012304 [quant-ph/0606161].
F.G.S.L. Brandão, A.W. Harrow and M. Horodecki, Local Random Quantum Circuits are Approximate Polynomial-Designs, Commun. Math. Phys. 346 (2016) 397 [arXiv:1208.0692].
F. Pastawski, B. Yoshida, D. Harlow and J. Preskill, Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence, JHEP 06 (2015) 149 [arXiv:1503.06237] [INSPIRE].
P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter and Z. Yang, Holographic duality from random tensor networks, JHEP 11 (2016) 009 [arXiv:1601.01694] [INSPIRE].
A.J. Scott, Optimizing quantum process tomography with unitary 2-designs, J. Phys. A 41 (2008) 055308 [arXiv:0711.1017].
B. Collins, Moments and cumulants of polynomial random variables on unitarygroups, the itzykson-zuber integral, and free probability, Int. Math. Res. Not. 2003 (2003) 953 [math-ph/0205010].
B. Collins and P. Śniady, Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group, Commun. Math. Phys. 264 (2006) 773 [math-ph/0402073].
D. Weingarten, Asymptotic Behavior of Group Integrals in the Limit of Infinite Rank, J. Math. Phys. 19 (1978) 999 [INSPIRE].
P. Diaconis and M. Shahshahani, On the eigenvalues of random matrices, J. Appl. Prob. 31 (1994) 49.
S. Bravyi, M.B. Hastings and F. Verstraete, Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order, Phys. Rev. Lett. 97 (2006) 050401 [quant-ph/0603121].
L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys. 64 (2016) 44 [arXiv:1403.5695] [INSPIRE].
A.R. Brown, D.A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Complexity, action and black holes, Phys. Rev. D 93 (2016) 086006 [arXiv:1512.04993] [INSPIRE].
X. Chen, Z.C. Gu and X.G. Wen, Local unitary transformation, long-range quantum entanglement, wave function renormalization and topological order, Phys. Rev. B 82 (2010) 155138 [arXiv:1004.3835] [INSPIRE].
D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].
Z.-C. Yang, A. Hamma, S.M. Giampaolo, E.R. Mucciolo and C. Chamon, Entanglement complexity in quantum many-body dynamics, thermalization, and localization, Phys. Rev. B 96 (2017) 020408 [arXiv:1703.03420].
E. Brézin and S. Hikami, Random Matrix Theory with an External Source, Springer Briefs in Mathematical Physics, Springer Singapore (2017).
Y. Huang, F.G. S.L. Brandao and Y.-L. Zhang, Finite-size scaling of out-of-time-ordered correlators at late times, arXiv:1705.07597 [INSPIRE].
M.V. Berry, Regular and irregular semiclassical wavefunctions, J. Phys. A 10 (1977) 2083.
M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50 (1994) 888 [cond-mat/9403051].
L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65 (2016) 239 [arXiv:1509.06411] [INSPIRE].
W.W. Ho and D. Radicevic, The Ergodicity Landscape of Quantum Theories, arXiv:1701.08777 [INSPIRE].
J. Sonner and M. Vielma, Eigenstate thermalization in the Sachdev-Ye-Kitaev model, arXiv:1707.08013 [INSPIRE].
J.M. Magan, Random free fermions: An analytical example of eigenstate thermalization, Phys. Rev. Lett. 116 (2016) 030401 [arXiv:1508.05339] [INSPIRE].
H. Gharibyan, M. Hanada, S. Shenker and M. Tezuka, to appear.
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
W. Brown and O. Fawzi, Decoupling with random quantum circuits, Commun. Math. Phys. 340 (2015) 867 [arXiv:1307.0632].
R.A. Low, Pseudo-randomness and Learning in Quantum Computation, Ph.D. Thesis (2010) [arXiv:1006.5227].
E. Brézin and S. Hikami, Extension of level-spacing universality, Phys. Rev. E 56 (1997) 264 [cond-mat/9702213].
R.E. Prange, The spectral form factor is not self-averaging, Phys. Rev. Lett. 78 (1997) 2280 [chao-dyn/9606010].