satunnaiskävelymalli

Satunnaiskävelymalli, known in English as the random walk model, is a mathematical concept describing a path that consists of a succession of random steps. Imagine a particle that moves from one point to another, where each movement is independent of the previous ones and follows a probability distribution. The direction and magnitude of each step are determined by chance.

The simplest form is a one-dimensional random walk, where a "walker" starts at a position and at each step moves either left or right with equal probability. This model has applications in various fields, including physics, where it can describe the diffusion of molecules, and finance, where it has been used to model stock prices. In computer science, random walks are employed in algorithms for graph traversal and sampling.

More complex versions exist, such as multi-dimensional random walks, where movements can occur in more than one direction. The behavior of a random walk over time can be analyzed using statistical methods. For instance, the expected distance from the starting point typically increases with the square root of the number of steps taken. While individual steps are unpredictable, the overall statistical properties of a long random walk can be quite regular.