The edge of random tensor eigenvalues with deviation
Abstract The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of order 3 and of size N, in the presence of a Gaussian n...
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| Format: | Article |
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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)071 |
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| author | Nicolas Delporte Naoki Sasakura |
| author_facet | Nicolas Delporte Naoki Sasakura |
| author_sort | Nicolas Delporte |
| collection | DOAJ |
| description | Abstract The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of order 3 and of size N, in the presence of a Gaussian noise, continuing the work [1], we compute the genuine and signed eigenvalue distributions, using field theoretic methods at large N combined with earlier rigorous results of [2]. We characterize the behaviour of the edge of the two distributions as the variance of the noise increases. We find two critical values of the variance, the first of which corresponding to the emergence of an outlier from the main part of the spectrum and the second where this outlier merges with the corresponding largest eigenvalue and they both become complex. We support our claims with Monte Carlo simulations. We believe that our results set the ground for a definition of pseudospectrum of random tensors based on Z-eigenvalues. |
| format | Article |
| id | doaj-art-7cfca0d20ba64ebda21fe6307829a72d |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-7cfca0d20ba64ebda21fe6307829a72d2025-01-19T12:07:42ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025112710.1007/JHEP01(2025)071The edge of random tensor eigenvalues with deviationNicolas Delporte0Naoki Sasakura1Okinawa Institute of Science and Technology Graduate UniversityYukawa Institute for Theoretical Physics, Kyoto UniversityAbstract The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of order 3 and of size N, in the presence of a Gaussian noise, continuing the work [1], we compute the genuine and signed eigenvalue distributions, using field theoretic methods at large N combined with earlier rigorous results of [2]. We characterize the behaviour of the edge of the two distributions as the variance of the noise increases. We find two critical values of the variance, the first of which corresponding to the emergence of an outlier from the main part of the spectrum and the second where this outlier merges with the corresponding largest eigenvalue and they both become complex. We support our claims with Monte Carlo simulations. We believe that our results set the ground for a definition of pseudospectrum of random tensors based on Z-eigenvalues.https://doi.org/10.1007/JHEP01(2025)071Effective Field TheoriesField Theories in Lower DimensionsNonperturbative EffectsRandom Systems |
| spellingShingle | Nicolas Delporte Naoki Sasakura The edge of random tensor eigenvalues with deviation Journal of High Energy Physics Effective Field Theories Field Theories in Lower Dimensions Nonperturbative Effects Random Systems |
| title | The edge of random tensor eigenvalues with deviation |
| title_full | The edge of random tensor eigenvalues with deviation |
| title_fullStr | The edge of random tensor eigenvalues with deviation |
| title_full_unstemmed | The edge of random tensor eigenvalues with deviation |
| title_short | The edge of random tensor eigenvalues with deviation |
| title_sort | edge of random tensor eigenvalues with deviation |
| topic | Effective Field Theories Field Theories in Lower Dimensions Nonperturbative Effects Random Systems |
| url | https://doi.org/10.1007/JHEP01(2025)071 |
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