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For a mere (uncorrelated) random walk, if the steps are constant and equal to 1 unit then for the distance from the starting point (net displacement): - the rms is equal to sqrt(n) in both 1 and 2 dimensions (the expected net squared displacement is equal to n) - the average distance asymptotes to sqrt(2n/pi) in 1 dimension but to sqrt(pi*n/4 ...
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.
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.
Walking simulators also known as exploration games are adventure games played often from the first-person perspective to explore an environment and to discover a narrative about the game, but often have little to no direct interaction with the environment itself.
An alternative view is that the distribution of a loop-erased random walk conditioned to start in some path β is identical to the loop-erasure of a random walk conditioned not to hit β. This property is often referred to as the Markov property of loop-erased random walk (though the relation to the usual Markov property is somewhat vague).
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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 ...
Random walk closeness centrality is a measure of centrality in a network, which describes the average speed with which randomly walking processes reach a node from other nodes of the network. It is similar to the closeness centrality except that the farness is measured by the expected length of a random walk rather than by the shortest path .
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