Statistical Theory of the Energy Levels of Complex Systems. I

By Freeman J. Dyson. 1962

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. D. Stanford
2. Alexei Borodin
3. Phil Saad
4. Jordan S. Cotler
5. E. Witten
6. Alex Kulesza
7. S. Shenker
8. G. Turiaci

Citations in the corpus

• Determinantal Point Processes for Machine Learning (2012, background): “In fact, years before Macchi gave them a general treatment, specific DPPs appeared in major results in random matrix theory [Mehta and Gaudin, 1960, Dyson, 1962a,b,c, Ginibre, 1965], where they continue to play an important role [Diaconis, 2003, Johansson, 2005b].”
• Light fields in complex media: Mesoscopic scattering meets wave control (2017, background): “× 𝑁∏︁ 𝑚<𝑛 |𝐸𝑛−𝐸𝑚|𝛽× 𝑁∏︁ 𝑛 exp[−𝐸2𝑛/(2𝑤2)] (29) is known as the Wigner-Dyson distribution, following the original work by these two authors (Dyson, 1962a; Wigner, 1957, 1967).”
• Random Matrix Theory and Fund of Funds Portfolio Optimisation (2007, background): “As of the end of the first quarter 2006 the total assets managed by hedge funds world wide is estimated at $1.25 trillion [1].”
• Anderson Transitions (2007, background): “Developing Wigner’s ideas, Dyson (1962) put forward a classification scheme of ensembles of random Hamiltonians.”
• Extreme value statistics of correlated random variables: A pedagogical review (2019, background): “Hence, this joint law can be interpreted as a Gibbs-Boltzmann weight [176] Pjoint({λi}) ∝ exp [−β E ({λi})], of an interacting gas of charged particles on a line where λi denotes the position of the i-th charge and β plays the role of the inverse temperature.”
• The Theory of Quantum Information (2018, background): “These definitions are rooted in the work of Dyson [64, 65, 66] and Diaconis and Shahshahani [60], and a more broad overview of random matrix theory may be found in the book of Mehta [156].”
• Supersymmetric SYK model and random matrix theory (2017, methodology): “We compute the level statistics of Q and compare it with the Wigner surmises of three standard Dyson – 18 – 1 ensembles in cases with different N .”
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos (2019, background): “13-(d), in comparison with numerical diagonalization of N = 4 CUE matrices, and in blue in Fig.”
• A Dynamical Approach to Random Matrix Theory (2017, unknown): “(This connection was exploited first in [46]).”