Speaker
Description
Random matrix theory has a long history of applications in the study of eigenvalue distributions arising in diverse real-world ensembles of matrix data. Matrix models also play a central role in theoretical particle physics, providing tractable mathematical models of gauge-string duality, and allowing the computation of correlators of invariant observables in physically interesting sectors of the AdS/CFT correspondence. A recent development is the definition of the general 13-parameter permutation invariant Gaussian matrix models and the computation of expectation values of permutation-invariant polynomials in these models. This was motivated by applications to the statistics of ensembles of generic real matrices arising from natural language processing and computational linguistics. For symmetric matrices with constant diagonals, such as arising in statistical finance, the general 4-parameter models have been similarly developed. Statistical tasks of symmetry-based data reduction, anomaly detection and similarity measurement for real-world entities represented by matrices have been successfully performed, by using the Gaussian models to test approximate Gaussianity and by quantifying the fine structure of departures from Gaussianity. Some of the matrix data analysed was generated by neural network methods. These applications have the potential to be extended into other areas of matrix data analysis, e.g. in collider particle physics.
Significance
The proposed talk would summarise the results from a sequence of 4 published papers and one arXiv preprint (please see list of references), and aims to initiate discussions with the particle physics community (phenomenological particle theorists and experimental particle physicists) on the application of the matrix data analysis method presented to matrix data in particle physics contexts.
References
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Dimitrios Kartsaklis, Sanjaye Ramgoolam, Mehrnoosh Sadrzadeh, ``Linguistic matrix theory,'' Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), no. 3, pp. 385–426
https://ems.press/journals/aihpd/articles/16212 \\\\\\\\\\\\\\\\\\\\\ -
Dimitrios Kartsaklis, Sanjaye Ramgoolam, Mehrnoosh Sadrzadeh, ``Linguistic matrix theory,'' Conference Proceedings, Quantum Physics and Logic, https://qpl.science.ru.nl/papers/QPL_2017_paper_29.pdf
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Sanjaye Ramgoolam, "Permutation invariant Gaussian matrix models," Nuclear Physics B, Volume 945, August 2019, 114682https://www.sciencedirect.com/science/article/pii/S0550321319301683
\\\\\\\\\\\\\\\\\\\\\\ - Sanjaye Ramgoolam, Mehrnoosh Sadrzadeh, and Lewis Sword, ``Gaussianity and typicality in matrix distributional semantics,'' Ann. Inst. H. Poincaré D Comb. Phys. Interact. 9 (2022), 1–45
https://ems.press/journals/aihpd/articles/5378510
\\\\\\\\\\\\\\\\\\\\\\ - Manuel Accettulli Huber, Adriana Correia, Sanjaye Ramgoolam, Mehrnoosh Sadrzadeh, ``Permutation invariant matrix statistics and computational language tasks,'' https://arxiv.org/abs/2202.06829
\\\\\\\\\\\\\\\\\\\\ - George Barnes, Sanjaye Ramgoolam, Michael Stephanou, ``Permutation invariant Gaussian matrix models for financial correlation matrices,''
Physica A: Statistical Mechanics and its Applications, Volume 651, 1 October 2024, 130015
https://www.sciencedirect.com/science/article/pii/S0378437124005247