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We prove non-perturbative bounds on the time evolution of the probability distribution of operator size in the $q$-local Sachdev-Ye-Kitaev model with $N$ fermions, for any even integer $q>2$ and any positive even integer $N>2q$.
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S. Sachdev and J. Ye · 1993
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“The large N N limit of superconformal field theories and supergravity”, Advances in Theoretical and Mathematical Physics
J. M. Maldacena · 1998
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“Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation”, Communications in Pure and Applied Mathematics
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Matrix Analysis and Applied Linear Algebra , (SIAM, 2000)
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M. C. Tran, C-F. Chen, A. Ehrenberg, A. Y. Guo, A. Deshpande, Y. Hong, Z-X. Gong, A. V. Gorshkov, and A. Lucas · 2001
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“Black holes and the butterfly effect”, Journal of High Energy Physics
S. H. Shenker and D. Stanford · 2014
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“A bound on chaos”, Journal of High Energy Physics
J. Maldacena, S. H. Shenker, and D. Stanford · 2016
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“Black holes and random matrices”, Journal of High Energy Physics
J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka · 2017
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M. Gärttner, J. G. Bohnet, A. Safavi-Naini, M. L. Wall, J. J. Bollinger, and A. M. Rey · 2017
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J. Li, R. Fan, H. Wan, B. Ye, B. Zeng, H. Zhai, X. Peng, and J. Du · 2017
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“Bekenstein-Hawking entropy and strange metals”, Physical Review
S. Sachdev · 2015
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“Models of AdS 2 \mathrm{AdS}_{2} backreaction and holography”, Journal of High Energy Physics
A. Almheiri and J. Polchinski · 2015
Cited alongside, same era.
“Comments on the Sachdev-Ye-Kitaev model”, Physical Review
J. Maldacena and D. Stanford · 2016
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“Chaos in AdS 2 \mathrm{AdS}_{2} holography”, Physical Review Letters
K. Jensen · 2016
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J. Maldacena, D. Stanford, and Z. Yang · 2016
Cited alongside, same era.
“Operator growth in the SYK model”, arXiv:1802.02633
D. A. Roberts, D. Stanford, and A. Streicher
Cited in the paper.
“Quantum epidemiology: operator growth, thermal effects, and SYK”, arXiv:1810.11958
X-L. Qi and A. Streicher
Cited in the paper.
A. Kitaev and S. J. Suh · 2018
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“Operator spreading in random unitary circuits”, Physical Review
A. Nahum, S. Vijay, and J. Haah · 2018
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C. W. von Keyserlingk, T. Rakovsky, F. Pollmann, and S. L. Sondhi · 2018
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A. Lucas · 2019
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“Fast scrambling on sparse graphs”, Proceedings of the National Academy of Sciences
G. Bentsen, Y. Gu, and A. Lucas · 2019
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“Fast scramblers”, Journal of High Energy Physics
Y. Sekino and L. Susskind · 2096
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