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Probability Theory and Random Point Processes Lab
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A probability theory lab that explores the arrangement of random points and the properties of graphs.
AboutAbout the lab
Reading random point configurations through mathematics
Within probability theory, the lab studies determinantal point processes, which describe how points are scattered at random.
By extracting the fermionic nature of eigenvalues of random matrices, the lab constructed this model of point configurations.
The lab is also interested in the relationships among random walks on graphs, the spectrum of the Laplacian, and the geometric properties of graphs.
Recently, the lab has also been studying random topology.
Key terms
- determinantal point process
- A model of random point configurations, also called a fermionic random field. Its starting point is the properties of the eigenvalues of random matrices
- random matrix
- A matrix whose entries are determined probabilistically. The arrangement of its eigenvalues is studied as a random point configuration
- random topology
- A field that uses probability theory to study topological properties, such as connectivity, of randomly constructed shapes and graphs
ResearchResearch themes
From the viewpoint of probability theory, the lab studies random point configurations and the properties of graphs. It constructs determinantal point processes by extracting a property seen in the eigenvalues of random matrices, and explores directions for generalizing them.
*Illustrative imageConstruction and generalization of determinantal point processes
The lab extracted the fermionic nature of eigenvalues of random matrices and built a model of random point configurations. It has become clear that representations of the infinite symmetric group and the distribution of zeros of random power series can also be described by this model.
*Illustrative imageGraphs and random topology
Focusing on the close mutual relationships among random walks on graphs, the spectrum of the Laplacian, and the geometric properties of graphs, the lab aims to clarify those relationships. Recently it has also been studying random topology.
MembersFaculty
- ProfessorTomoyuki Shirai
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: “Assortative Case of the SBM” Rosey9921 / CC BY-SA 4.0 (cropped)
- Construction and generalization of determinantal point processes: “Relation (cubic matrix)” WatchduckYou can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck". / CC BY 3.0 (cropped)
- Graphs and random topology: “Random regular graph” Gaetano Cirianni / CC BY-SA 4.0 (cropped)
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学 （富安 （大石） 亮子） ): “Rendering of quasicrystal structure” LinKayser / CC BY-SA 4.0 (cropped) - Related lab (〈位相幾何学・
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