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Okada Lab
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The lab uses probability theory to study the behavior of random walks.
AboutAbout the lab
Exploring the structure hidden in random steps
The Okada Lab uses probability theory to study the long-time behavior of Markov processes.
The lab investigates, from a probabilistic perspective, the fundamental properties of simple random walks on the integer lattice and of Brownian motion, their continuous-time version.
The objects of study include hitting probabilities, intersections, and local times.
In particular, the lab examines the geometric structure of thick points, the exceptional points at which the local time of a random walk takes large values.
Key terms
- Markov process
- A stochastic process in which the next move depends only on the current state, not on the path taken so far
- Random walk
- A model of a point that moves by choosing the direction of each step at random
- Local time
- A quantity that measures how long a random walk or similar process stays at a given location
ResearchResearch themes
The lab uses probability theory to study the long-time behavior of Markov processes. It investigates properties of simple random walks on the integer lattice and of Brownian motion, such as hitting probabilities, intersections, and local times.
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MembersFaculty
- Associate ProfessorIzumi OkadaPublications ↗
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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: “2D Random Walk Trace” Purpy Pupple / CC BY-SA 3.0 (cropped)
- Long-Time Behavior of Markov Processes: “Local times surface” Roboquant / CC BY 3.0 (cropped)
- Related lab (Aida Lab): “BMonSphere” Thomas Steiner / CC BY-SA 2.5 (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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