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Aida Lab
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A lab that develops infinite-dimensional analysis based on the measure of Brownian motion.

AboutAbout the lab
Analyzing probability in infinite-dimensional spaces.
Aida Lab studies probability theory from the perspective of infinite-dimensional analysis.
The lab has investigated operators on loop spaces and Hamiltonians that arise in quantum field theory, examining properties such as their spectra and semiclassical limits.
Rough path analysis, as well as differential equations driven by rough paths and the approximation of solutions to stochastic differential equations, is also among its research subjects.
Key terms
- Brownian motion
- A mathematical description of the irregular movement of tiny particles suspended in water. It is a fundamental object in probability theory.
- Loop space
- The space consisting of all curves (loops) on a given shape whose starting point and endpoint coincide. It is infinite-dimensional.
- Rough path analysis
- A theory for handling differential equations that evolve along highly jagged, irregular paths.
ResearchResearch themes
The lab's field is probability theory, and its research theme is the study of probability theory from the viewpoint of infinite-dimensional analysis. In addition to analysis on infinite-dimensional spaces, the lab is interested in functional inequalities and also studies rough path analysis.
View More ↗MembersFaculty
- ProfessorShigeki AidaPublications ↗
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Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Aida Lab
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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: “BMonSphere” Thomas Steiner / CC BY-SA 2.5 (cropped)
- Probability Theory from the Viewpoint of Infinite-Dimensional Analysis: “Wiener process 3d” Sullivan.t.j / CC BY-SA 3.0 (cropped)
- Related lab (Okada Lab): “2D Random Walk Trace” Purpy Pupple / CC BY-SA 3.0 (cropped)
- Related lab (Sasada Lab): “Brownien2d3000pts” Ipipipourax / CC0 (cropped)
- Related lab (Koike Lab): “Tickers ( )” Francisco Gonzalez / CC BY 2.0 (cropped)
- Related lab (Masuda Lab): “NIG-process” Thomas Steiner and Martin Keller-Ressel / CC BY-SA 2.5 (cropped)
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