publication . Preprint . 2020

On the generalization of the Wigner semicircle law to real symmetric tensors

Gurau, Razvan;
Open Access English
  • Published: 21 Apr 2020
  • Publisher: HAL CCSD
  • Country: France
Abstract
Comment: v2, references added
Subjects
free text keywords: Borel transformation, Wigner, density: spectral, spin: model, tensor, expansion 1/N, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Mathematical Physics, High Energy Physics - Theory, 60B99
Funded by
EC| RTFT
Project
RTFT
Random Tensors and Field Theory
  • Funder: European Commission (EC)
  • Project Code: 818066
  • Funding stream: H2020 | ERC | ERC-COG
26 references, page 1 of 2

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[4] L. Qi, Eigenvalues of a real supersymmetric tensor, Journal of Symbolic Computation 40 (2005), no. 6 1302-1324.

[5] C.-F. Cui, Y.-H. Dai and J. Nie, All real eigenvalues of symmetric tensors, SIAM Journal on Matrix Analysis and Applications 35 (2014), no. 4 1582-1601.

[6] D. Cartwright and B. Sturmfels, The number of eigenvalues of a tensor, Linear algebra and its applications 438 (2013), no. 2 942-952.

[7] O. Evnin, Melonic dominance and the largest eigenvalue of a large random tensor, arXiv:2003.11220.

[8] R. Gurau, Universality for Random Tensors, Ann. Inst. H. Poincar´e Proba. Stat. 50 (2014), no. 4 1474-1525 [arXiv:1111.0519].

[9] G. B. Arous, S. Mei, A. Montanari and M. Nica, The landscape of the spiked tensor model, Communications on Pure and Applied Mathematics 72 (2019), no. 11 2282-2330.

[10] L. Qi, Eigenvalues and invariants of tensors, Journal of Mathematical Analysis and Applications 325 (2007), no. 2 1363-1377.

[11] V. Ros, Distribution of rare saddles in the p-spin energy landscape, Journal of Physics A: Mathematical and Theoretical 53 (mar, 2020) 125002. [OpenAIRE]

[12] P. Breiding, How many eigenvalues of a random symmetric tensor are real?, Transactions of the American Mathematical Society 372 (2019), no. 11 7857-7887. [OpenAIRE]

[13] P. Breiding, The expected number of eigenvalues of a real gaussian tensor, SIAM Journal on Applied Algebra and Geometry 1 (2017), no. 1 254-271. [OpenAIRE]

[14] B. Collins and P. Sniady, Integration with respect to the Haar measure on unitary, orthogonal and symplectic group, Commun. Math. Phys. 264 (2006) 773 [arXiv:0402073]. [OpenAIRE]

[15] J. Ben Geloun and S. Ramgoolam, Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras, JHEP 11 (2017) 092 [arXiv:1708.03524].

26 references, page 1 of 2
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publication . Preprint . 2020

On the generalization of the Wigner semicircle law to real symmetric tensors

Gurau, Razvan;