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Hamana Lab
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A probability theory lab that uses mathematics to capture random motion.
AboutAbout the lab
Investigating random motion mathematically.
The Hamana Lab studies stochastic process theory and stochastic analysis within probability theory.
Probability theory is not just about counting cases when rolling dice; it takes natural phenomena as its subject and is one of the major pillars supporting modern mathematics.
From a probabilistic viewpoint, the lab investigates the motion of particles in materials containing impurities, and the behavior of quantities that change randomly over time.
Probability theory is described as a broad field that is connected not only to other areas of mathematics but also to biology, engineering, and economics.
Key terms
- Random walk
- A simple model in which a particle moves randomly on a square lattice
- Diffusion process
- A quantity that changes randomly over time. It is often expressed using stochastic differential equations
- Brownian motion
- An example of a diffusion process. It is named after Brown, who observed the irregular motion of fine particles in water
ResearchResearch themes
This lab studies random motion, such as random walks and diffusion processes, as objects of mathematics. It tackles questions such as how the motion of a particle changes when impurities are present, and what the time is at which a diffusion process first reaches a given set.
*Illustrative imageGlobal properties of random walks
The lab considers how the motion of a particle differs between cases without impurities and cases with impurities. The condition under which a random walk on a square lattice returns to its starting point with probability 1 has been settled in one dimension, but in higher dimensions it has been settled only in special situations.
*Illustrative imageHitting times of diffusion processes
The lab studies the time at which a diffusion process first reaches a given set. For Brownian motion, quantities such as the distribution function of the hitting time have been obtained, and similar information has been obtained for Brownian motion with constant drift. Multidimensional diffusion processes are a field still under development.
MembersFaculty
- ProfessorYuji Hamana
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: “Notions-of-convergence-in-probability-theory” Emptiless / Public domain (cropped)
- Global properties of random walks: “Tabuleiros de Galton (antes e depois)” Exhibit made by Estes Objethos Atelier, photo by Rodrigo Tetsuo Argenton / CC BY-SA 4.0 (cropped)
- Hitting times of diffusion processes: “Brownian trajectory” Roque345 / CC BY 3.0 (cropped)
- Related lab (福島 竜輝 研究室): “Walk3d 2” No machine-readable author provided. Zweistein~commonswiki assumed (based on copyright claims). / CC BY 2.5 (cropped)
- Related lab (塩谷 真弘 研究室): “Symbolic Logic Carroll” Lewis Carroll / Public domain (cropped)
- Related lab (松浦 浩平 研究室): “Random walk in1d” Flomenbom / CC BY-SA 3.0 (cropped)
- Related lab (竹内 耕太 研究室): “Classroom blackboard at Cornell University, Ithaca, NY 25” LBM1948 / CC BY-SA 4.0 (cropped)
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