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Nagao Lab
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The lab explores the fundamental theory and applications of random matrices, whose entries are random numbers.
AboutAbout the lab
From matrices of random numbers to mathematics that spans fields.
Prof. Nagao studies the theory of random matrices and their applications.
A random matrix is a matrix whose entries are random numbers; the concept was conceived in the field of mathematical statistics at the beginning of the 20th century.
Today it is widely applied across many fields, including analytic number theory, elementary particle physics, solid-state physics, ecology, and financial engineering.
The lab aims to deepen the fundamental theory by opening up new application areas, and to create a cycle in which that development in turn gives rise to new applications.
Key terms
- Random matrix
- A matrix whose entries are determined by random numbers. Properties such as the arrangement of its eigenvalues are studied in the language of probability.
- Energy level
- In quantum mechanics, one of the discrete energy values that a system such as an atom can take.
- Chaos
- Motion that follows fixed laws, yet in which tiny differences at the start grow large, making long-term prediction difficult.
ResearchResearch themes
The lab pursues random matrix theory from multiple angles, from both the fundamental mathematics and a range of applications. Drawing on real-world problems as a source of ideas, it aims to deepen understanding of the underlying mathematics.
*Illustrative imageRandom matrix theory and its applications
Random matrices were introduced into nuclear physics after World War II, and their applications have since spread to analytic number theory, elementary particle physics, and solid-state physics, among others. The lab studies them from both fundamental and applied sides, including the mathematics of eigenvalue correlations.
*Illustrative imageSemiclassical theory of energy level statistics
The energy levels of a quantum system reflect properties of the corresponding classical mechanics. When the classical system is chaotic, universal level correlations are observed; to clarify the cause of this universality, the lab studies the relationship between semiclassical quantum theory and random matrices.
MembersFaculty
- ProfessorTaro Nagao
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Assorted dice for games, 2024” Ironmaidenfun / CC BY-SA 4.0 (cropped)
- Random matrix theory and its applications: “Matriz organizacao” Silveiraneto at Portuguese Wikipedia / Public domain (cropped)
- Semiclassical theory of energy level statistics: “Dispersion Dots” Rossmantj / CC0 (cropped)
- Related lab (Nakashima Lab): “Galton-watson(poisson(1),11gen, 47noeud)” Ipipipourax, S. Roger / CC0 (cropped)
- Related lab (Mathematical Physics, Statistical Mechanics, and Condensed Matter Theory Lab): “2D-Hubbard-model” Susumu Yamada, Toshiyuki Imamura, Masahiko Machida / CC BY-SA 4.0 (cropped)
- Related lab (Representation Theory and Infinite-Dimensional Integrable Systems Lab): “Dynkin diagram Dn” Rogilbert / Public domain (cropped)
- Related lab (Information Theory, Quantum Information Theory, Theoretical Computer Science, and Algorithm Theory Lab (Ryuhei Mori)): “Quantum Computer with Dispersive Background 2” OJB Quantum / CC BY 4.0 (cropped)
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