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Infinite Analysis Research Division (Croydon) Lab
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The lab is a probability theory lab that studies random walks in random environments.
AboutAbout the lab
Exploring random walks in random environments
The Croydon Lab studies probability theory, in particular random walks in random environments.
Its main interest is diffusion processes on random fractals and their construction as scaling limits of random walks on random graphs.
Its interests also extend to the behavior of discrete integrable systems started from random initial conditions.
Key terms
- Random walk
- A model of the motion of a point that chooses its direction of movement at random at each step
- Fractal
- A shape in which forms similar to the whole repeatedly appear in its details, however much it is magnified. The Sierpinski gasket is a typical example.
- Scaling limit
- A continuous motion obtained by taking a limit, while changing the scale, of motion on a fine mesh
NewsLab news
View More ↗ResearchResearch themes
The lab studies probability theory, particularly random walks in random environments. This field is motivated by topics such as disordered media in physics and complex networks in computer science, and the lab investigates diffusion processes on random fractals and random walks on random graphs.
*Illustrative imageThe transition from fractal to Euclidean
In joint research, the lab established the scaling limits of the diffusion processes and their transition densities for variants of the Sierpinski gasket that approach the unit triangle.
*Illustrative imageCollisions on random walk trajectories
In joint research, the lab studied the collision of two or three random walks on the random graph formed by the trajectory of a four-dimensional random walk.
MembersFaculty
- Associate ProfessorDavid Croydon
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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: “Schramm-Loewner Evolution” Tesseract16 / CC0 (cropped)
- The transition from fractal to Euclidean: “Sierpiński triangle transforming into a T-square fractal” MagistraMundi / CC BY-SA 4.0 (cropped)
- Collisions on random walk trajectories: “2D Random Walk” Asolorozc01 / CC BY-SA 4.0 (cropped)
- Related lab (Infinite Analysis Lab (Naotaka Kajino)): “Pseudo Kleinian OpenCL K 002” PantheraLeo1359531 / CC BY-SA 4.0 (cropped)
- Related lab (Infinite Analysis Lab (Odaka)): “Quartic Fermat curve” Jacob Rus / CC BY-SA 4.0 (cropped)
- Related lab (Infinite Analysis Lab (Ogata)): “Thousands of Atoms Swap 'Spins' with Partners in Quantum Square Dance ( )” National Institute of Standards and Technology / Public domain (cropped)
- Related lab (Tamagawa Lab): “Klein-map” PSL27 / CC BY-SA 4.0 (cropped)
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