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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. (animated version)In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some mathematical space.
In mathematics, a continuous-time random walk (CTRW) is a generalization of a random walk where the wandering particle waits for a random time between jumps. It is a stochastic jump process with arbitrary distributions of jump lengths and waiting times.
Maze generation animation using Wilson's algorithm (gray represents an ongoing random walk). Once built the maze is solved using depth first search. All the above algorithms have biases of various sorts: depth-first search is biased toward long corridors, while Kruskal's/Prim's algorithms are biased toward many short dead ends.
Maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the principle of maximum entropy, which says that the probability distribution which best represents the current state of knowledge is the one with largest entropy.
Quantum random circuits (QRC) is a concept of incorporating an element of randomness into the local unitary operations and measurements of a quantum circuit. The idea is similar to that of random matrix theory which is to use the QRC to obtain almost exact results of non-integrable, hard-to-solve problems by averaging over an ensemble of outcomes.
The pivot algorithm works by taking a self-avoiding walk and randomly choosing a point on this walk, and then applying symmetrical transformations (rotations and reflections) on the walk after the n th step to create a new walk. Calculating the number of self-avoiding walks in any given lattice is a common computational problem. There is ...
A Lévy flight is a random walk in which the step-lengths have a stable distribution, [1] a probability distribution that is heavy-tailed. When defined as a walk in a space of dimension greater than one, the steps made are in isotropic random directions. Later researchers have extended the use of the term "Lévy flight" to also include cases ...
In probability theory, a branching random walk is a stochastic process that generalizes both the concept of a random walk and of a branching process. At every generation (a point of discrete time ), a branching random walk's value is a set of elements that are located in some linear space , such as the real line .
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