The phenomenon of mathematics, known as Random Walk, is used to describe the path consisting of the sum of random steps taken in any mathematical space. Random Walk, used in many areas, is used to predict the movements of things that move independently. Some scientists working on Random Walk thought it was a random walk in areas with random dimensions and geometries. Scientists from the California Institute of Technology (Caltech) have determined that, unlike these scientists, objects with very different geometries are random walk in groups. After a certain time has passed in the Random Walk of certain groups, the path of the walk will unite in a certain direction. In this case, it can be thought that objects that perform Random Walk perform a path-dependent walk. The fact that the walk depends on the road indicates that the outcome of something that was at the beginning was determined by the road. Omer Tamuz, a professor of economics and mathematics in Caltech, explains his solutions for the Random Walk they found through two hypothetical communities. Tamuz gives an example of two communities, one of which has shown technological advances and the other has experienced major natural disasters. Tamuz said, “These two societies forget all their experiences and can they unite at some point?” she asks. Tamuz says it is known that there are communities with such Random Walk memories of their past, while other communities have lost their memory. However, it was not clear which groups had this memory and which were not. The work of researchers from Caltech eliminates this problem. The researchers determined that there was a geometrical way of defining the characteristics of the groups to solve this problem. “Think about a circle to understand the essence of it,” said researcher Omer Tamuz. You can define the circle geometrically or by an algebraic equation. When it comes to Random Walk, what needs to be done is the use of geometrical and algebraic features. ” Researchers from Caltech solved the problem in the Random Walk model with groups whose geometric or algebraic properties were determined. Mathematicians say that once the connection between groups and geometric shapes is understood, it is much easier to solve the problem.
