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Analysis Lab (Takahiro Hasebe)
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The lab studies free probability, a field centered on probability theory in which combinatorics and functional analysis merge.
AboutAbout the lab
Noncommutative probability, where many fields merge.
Prof. Hasebe studies probability theory, combinatorics, graph theory, functional analysis, complex analysis, and representation theory, with probability theory at the center.
Particular emphasis is placed on noncommutative probability (free probability).
This field is something like a fusion of all the fields listed above, and Prof. Hasebe writes that it suits students who like mathematics broadly without narrowing their specialization too much.
Current interests are free probability, branching processes, and topology optimization.
Key terms
- Free probability
- A theory that extends ordinary probability theory to the noncommutative world. It is deeply connected to combinatorics and functional analysis
- Random matrix
- A matrix whose entries are chosen at random. Studying the behavior of its eigenvalues is a fundamental problem
- Stochastic process
- A quantity that changes randomly over time. Brownian motion is a representative example
ResearchResearch themes
The lab covers probability theory, combinatorics, graph theory, functional analysis, complex analysis, and representation theory, with probability theory at the center. Most students who join the lab first study probability theory.
*Illustrative imageStochastic Processes and Stochastic Differential Equations
The lab covers stochastic processes such as Brownian motion, stochastic differential equations, and the theory of the Itô integral. Because stochastic processes are closely tied to statistical physics and quantum physics, the professor recommends studying these fields as well.
*Illustrative imageRandom Graphs and Random Matrices
This field examines what phenomena occur when a graph is given randomly, such as the expected number of connected components and the size of the largest connected component. In random matrices, the study of eigenvalues is a fundamental problem.
*Illustrative imageNoncommutative Probability (Free Probability)
This is the professor's specialty. The theory of quantum physics is built in such a way that it cannot avoid the concept of "probability," and it is known that ordinary probability theory is not enough. Noncommutative probability provides the mathematical foundation for this, and research as pure mathematics apart from physics is also active.
MembersFaculty
- Associate ProfessorTakahiro Hasebe
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: “Fig sinc” Sergey69 / CC BY-SA 3.0 (cropped)
- Stochastic Processes and Stochastic Differential Equations: “Wiener process 3d” Sullivan.t.j / CC BY-SA 3.0 (cropped)
- Random Graphs and Random Matrices: “Erdos generated network-p0.01” w:User:Vonfrisch / CC BY-SA 3.0 (cropped)
- Noncommutative Probability (Free Probability): “Rabbit-lamination” Adam majewski / CC BY-SA 3.0 (cropped)
- Related lab (Algebra (Travis Scrimshaw) Lab): “E10 e8coxeterplane height120” Teake Nutma / CC BY 3.0 (cropped)
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