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- Heterogeneous_random_walk_in_one_dimension abstract "In studies of dynamics, probability, physics, chemistry and related fields, a heterogeneous random walk in one dimension (also termed: Heterogeneous random walk in 1d, one-dimensional heterogeneous random walk, etc.) is a random walk in a one dimensional interval with jumping rules that depend on the location of the random walker in the interval.For example: say that the time is discrete and also the interval. Namely, the random walker jumps every time step either left or right. A possible heterogeneous random walk draws in each time step a random number that determines the local jumping probabilities and then a random number that determines the actual jump direction. Specifically, say that the interval has 9 sites (labeled 1 through 9), and the sites (also termed states) are connected with each other linearly (where the edges sites are connected their adjacent sites and together). In each time step, the jump probabilities (from the actual site) are determined when flipping a coin; for head we set: probability jumping left =1/3, where for tail we set: probability jumping left = 0.55. Then, a random number is drawn from a uniform distribution: when the random number is smaller than probability jumping left, the jump is for the left, otherwise, the jump is for the right. Usually, in such a system, we are interested in the probability of staying in each of the various sites after t jumps, and in the limit of this probability when t is very large, .Generally, the time in such processes can also vary in a continuous way, and the interval is also either discrete or continuous. Moreover, the interval is either finite or without bounds. In a discrete system, the connections are among adjacent states. The basic dynamics are either Markovian, semi-Markovian, or even not Markovian depending on the model. In discrete systems, 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 location in the system.General solutions for heterogeneous random walks in 1d obey equations (1)-(5), presented in what follows.".
- Heterogeneous_random_walk_in_one_dimension thumbnail Random_walk_in1d.jpg?width=300.
- Heterogeneous_random_walk_in_one_dimension wikiPageID "31907287".
- Heterogeneous_random_walk_in_one_dimension wikiPageRevisionID "580730559".
- Heterogeneous_random_walk_in_one_dimension hasPhotoCollection Heterogeneous_random_walk_in_one_dimension.
- Heterogeneous_random_walk_in_one_dimension subject Category:Statistical_mechanics.
- Heterogeneous_random_walk_in_one_dimension subject Category:Stochastic_processes.
- Heterogeneous_random_walk_in_one_dimension subject Category:Variants_of_random_walks.
- Heterogeneous_random_walk_in_one_dimension type Abstraction100002137.
- Heterogeneous_random_walk_in_one_dimension type Cognition100023271.
- Heterogeneous_random_walk_in_one_dimension type Concept105835747.
- Heterogeneous_random_walk_in_one_dimension type Content105809192.
- Heterogeneous_random_walk_in_one_dimension type Hypothesis105888929.
- Heterogeneous_random_walk_in_one_dimension type Idea105833840.
- Heterogeneous_random_walk_in_one_dimension type Model105890249.
- Heterogeneous_random_walk_in_one_dimension type PsychologicalFeature100023100.
- Heterogeneous_random_walk_in_one_dimension type StochasticProcess113561896.
- Heterogeneous_random_walk_in_one_dimension type StochasticProcesses.
- Heterogeneous_random_walk_in_one_dimension comment "In studies of dynamics, probability, physics, chemistry and related fields, a heterogeneous random walk in one dimension (also termed: Heterogeneous random walk in 1d, one-dimensional heterogeneous random walk, etc.) is a random walk in a one dimensional interval with jumping rules that depend on the location of the random walker in the interval.For example: say that the time is discrete and also the interval. Namely, the random walker jumps every time step either left or right.".
- Heterogeneous_random_walk_in_one_dimension label "Heterogeneous random walk in one dimension".
- Heterogeneous_random_walk_in_one_dimension sameAs m.0gvtx8b.
- Heterogeneous_random_walk_in_one_dimension sameAs Q5747218.
- Heterogeneous_random_walk_in_one_dimension sameAs Q5747218.
- Heterogeneous_random_walk_in_one_dimension sameAs Heterogeneous_random_walk_in_one_dimension.
- Heterogeneous_random_walk_in_one_dimension wasDerivedFrom Heterogeneous_random_walk_in_one_dimension?oldid=580730559.
- Heterogeneous_random_walk_in_one_dimension depiction Random_walk_in1d.jpg.
- Heterogeneous_random_walk_in_one_dimension isPrimaryTopicOf Heterogeneous_random_walk_in_one_dimension.
