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Probability Theory Lab
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A research field that uses mathematics to unravel random phenomena through probability theory.
AboutAbout the lab
Solving randomness in the language of mathematics.
The probability theory field studies probability theory, the mathematical framework for logically analyzing random phenomena.
Because the world is full of many kinds of randomness, probability theory has become a research field of wide scope.
Each faculty member works on a different subject, such as stochastic analysis, point processes, quantum field theory, and interacting particle systems.
Key terms
- Rough path theory
- A theory that views the theory of stochastic differential equations from a different angle. It allows line integrals along irregular continuous paths to be formulated without probability theory
- Determinantal point process
- A random configuration of points constructed by abstracting the fermionic nature of the eigenvalues of random matrices.
- Quantum field theory
- From a mathematical standpoint, the Hamiltonians that appear in quantum field theory are regarded as unbounded self-adjoint operators and studied as such
ResearchResearch themes
The probability theory field studies theories for analyzing random phenomena mathematically. Each faculty member works on subjects such as stochastic differential equations, random configurations of points, and the spectra of quantum field theory.
*Illustrative imageRough Path Theory and Stochastic Differential Equations
Prof. Inahama studies rough path theory from the standpoint of stochastic analysis. It is a theory that views Itô's stochastic differential equations from a different angle, and it also uses Malliavin calculus.
*Illustrative imageRandom Configurations of Points and Graphs
Prof. Shirai constructs determinantal point processes, which abstract the fermionic nature of the eigenvalues of random matrices, and explores their generalizations. He also studies random walks on graphs, the spectra of Laplacians, and random topology.
Spectral Analysis in Quantum Field Theory
Prof. Hiroshima analyzes the spectra of Hamiltonians that appear in quantum field theory from a mathematical standpoint. The goal is to investigate matters such as the existence of ground states and estimates of their degeneracy, using operator theory, stochastic analysis, and functional integrals.
MembersFaculty
- ProfessorYuzuru Inahama
- ProfessorTomoyuki Shirai
- ProfessorFumio Hiroshima
- Associate ProfessorKenkichi Tsunoda
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: “Set Estimation from Reflected Brownian Motion 02” MGromov / CC BY-SA 4.0 (cropped)
- Rough Path Theory and Stochastic Differential Equations: “Brownian trajectory” Roque345 / CC BY 3.0 (cropped)
- Random Configurations of Points and Graphs: “Assortative Case of the SBM” Rosey9921 / CC BY-SA 4.0 (cropped)
- Related lab (Optimization Lab): “Undirected NetworkX Graph” KalebD07 / CC0 (cropped)
- Related lab (Differential Equations Lab): “Gradient Vector Flow 3D Metasphere Example Result” YoungX2040 / CC BY-SA 4.0 (cropped)
- Related lab (Dynamical Systems Lab): “Lorenz caos3” António Miguel de Campos / Public domain (cropped)
- Related lab (Topology Lab): “Klein bottle green” Aizenr / CC BY-SA 4.0 (cropped)
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