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Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase and ergodic transition have a status of a mathematical theorem.
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I. M. Khaymovich, J. V. Koski, O.-P. Saira, V. E. Kravtsov, and J. P. Pekola, “Multifractality of random eigenfunctions and generalization of Jarzynski equality,” Nature Comms. 6
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E. Bogomolny and M. Sieber, “Power-law random banded matrices and ultrametric matrices: Eigenvector distribution in the intermediate regime,” Phys. Rev. E 98
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2019
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M Pino, J Tabanera, and P Serna, “From ergodic to non-ergodic chaos in Rosenzweig–Porter model,” Journal of Physics A: Mathematical and Theoretical 52
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2016
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D. Facoetti, P. Vivo, and G. Biroli, “From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective,” Europhys. Lett. 115
2016
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K. Truong and A. Ossipov, “Eigenvectors under a generic perturbation: Non-perturbative results from the random matrix approach,” Europhys. Lett. 116
2016
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E. Tarquini, G. Biroli, and M. Tarzia, “Level statistics and localization transitions of lévy matrices,” Phys. Rev. Lett. 116
2016
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I. García-Mata, O. Giraud, B. Georgeot, J. Martin, R. Dubertrand, and G. Lemarié, “Scaling theory of the anderson transition in random graphs: Ergodicity and universality,” Phys. Rev. Lett. 118
2017
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M. Amini, “Spread of wave packets in disordered hierarchical lattices,” Europhys. Lett. 117
2017
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C. Monthus, “Statistical properties of the green function in finite size for anderson localization models with multifractal eigenvectors,” J. Phys. A: Math. Theor. 50
2017
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M. Pino, V. E. Kravtsov, B. L. Altshuler, and L. B. Ioffe, “Multifractal metal in a disordered Josephson junctions array,” Phys. Rev. B 96
2017
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2019
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P. A. Nosov, I. M. Khaymovich, and V. E. Kravtsov, “Correlation-induced localization,” Physical Review B 99
2019
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Giuseppe de Tomasi, Moshen Amini, Soumya Bera, Ivan M. Khaymovich, and Vladimir E. Kravtsov, “Survival probability in Generalized Rosenzweig-Porter random matrix ensemble,” SciPost Phys. 6
2019
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P. A. Nosov and I. M. Khaymovich, “Robustness of delocalization to the inclusion of soft constraints in long-range random models,” Phys. Rev. B 99
2019
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V Avetisov, A Gorsky, S Nechaev, and O Valba, “Localization and non-ergodicity in clustered random networks,” Journal of Complex Networks (2019), 10.1093/comnet/cnz026 , cnz026
2019
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I. M. Khaymovich, M. Haque, and P. A. McClarty, “Eigenstate thermalization, random matrix theory, and behemoths,” Phys. Rev. Lett. 122
2019
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Arnd Bäcker, Masudul Haque, and Ivan M Khaymovich, “Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems,” Phys. Rev. E 100
2019
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Vadim N. Smelyanskiy, Kostyantyn Kechedzhi, Sergio Boixo, Sergei V. Isakov, Hartmut Neven, and Boris Altshuler, “Nonergodic delocalized states for efficient population transfer within a narrow band of the energy landscape,” Phys. Rev. X 10
2020
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I. García-Mata, J. Martin, R. Dubertrand, O. Giraud, B. Georgeot, and G. Lemarié, “Two critical localization lengths in the anderson transition on random graphs,” Phys. Rev. Research 2
2020
Closest in time.
I. M. Khaymovich and V. E. Kravtsov, (2020), (unpublished)
2020
Closest in time.