Posts
- Researchers used algebra and geometry together to solve an old random walk problem.
- Random walk ideas have informed everything from biology to video games.
- This team identified a key geometry idea that unites some random walks and sets others apart.
It's a breakthrough in the field of random walks, explains Caroline Delbert, writer, book editor, researcher, and avid reader.
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| Five eight-step random walks from a central point. Some paths appear shorter than eight steps where the route has doubled back on itself. Photo: Creative Commons |
Mathematicians from the California Institute of Technology have solved an old problem related to a mathematical process called a random walk.
The
team, which also worked with a colleague from Israel’s Ben-Gurion
University, solved the problem in a rush after having a realization one
evening. Lead author Omer Tamuz studies both economics and mathematics,
using probability theory and ergodic theory as the link—a progressive
and blended approach that this year’s Abel Prize-winning mathematicians helped to trailblaze.
Tamuz said in a Caltech statement that he’d explained a potential
breakthrough to his students one day, then found out the next day they’d
gone ahead and solved it...
The idea and principles of random walk theory are used across many disciplines. Biologists can use random walks to model how animals move and behave. Physicists use it to describe and model how particles behave.
And learning how to implement versions of it has been an ongoing
project for computer scientists. Some random walks appear to behave
according to where they’ve already been, which is called being path dependent. Others seem to ignore their “pasts” and end up converging with other paths with different histories.
Source: Popular Mechanics
