A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modeled as random walks, although they may not be truly random in reality. The term random walk was first introduced by Karl Pearson in 1905. Random walks have been used in many fields: ecology, economics, psychology, computer science, physics, chemistry, and biology. Random walks explain the observed behaviors of processes in these fields, and thus serve as a fundamental model for the recorded stochastic activity.
Various different types of random walks are of interest. Often, random walks are assumed to be Markov chains or Markov processes, but other, more complicated walks are also of interest. Some random walks are on graphs, others on the line, in the plane, or in higher dimensions, while some random walks are on groups. Random walks also vary with regard to the time parameter. Often, the walk is in discrete time, and indexed by the natural numbers, as in . However, some walks take their steps at random times, and in that case the position is defined for the continuum of times . Specific cases or limits of random walks include the Lévy flight. Random walks are related to the diffusion models and are a fundamental topic in discussions of Markov processes. Several properties of random walks, including dispersal distributions, first-passage times and encounter rates, have been extensively studied.
Other articles related to "random walk, random walks, random":
... Heterogeneous random walks in one dimension can have either discrete time or continuous time ... Heterogeneous random walks in 1D have jump probabilities that depend on the location in the system, and/or different jumping time (JT) probability density functions (PDFs) that depend on the ... Known important results in simple systems include In a symmetric Markovian random walk, the Green's function (also termed the PDF of the walker) for occupying state ...
... In A Random Walk Down Wall Street, Burton Malkiel (b ... University, argues that asset prices typically exhibit signs of random walk and that one cannot consistently outperform market averages ... Random walk is a theory about the movement of stock and commodity futures prices hypothesizing that past prices are of no use in forecasting future price movements ...
... simply start at one vertex and perform a random walk until you find the other one (then accept) or until
... The technique of simulated annealing is based on changing the probability of doing a random move over one that maximally decreasing the cost ... name originates from the strategy of decreasing the probability of doing random moves during the execution of the algorithm, thus virtually "freezing" the space of search ... Simulated annealing decreases this temperature over time, thus allowing more random moves at the beginning and less after time ...
Famous quotes containing the words walk and/or random:
“From the time the Englishmans bones harden into bones at all, he makes his skeleton a flagstaff, and he early plants his feet like one who is to walk the world and the decks of all the seas.”
—Willa Cather (18761947)
“Novels as dull as dishwater, with the grease of random sentiments floating on top.”
—Italo Calvino (19231985)