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Related to ergodic: Ergodic hypothesis


Of or relating to a system or process whose overall statistical properties can be determined by analysis of a sufficiently large sample of the states of one of its constituents or instances averaged over time.

[German Ergode, a set of points in a space with the property that all points will be included in a trajectory with equal frequency given a sufficient large number of trajectories (coined by Ludwig Eduard Boltzmann from Greek ergon, work; see werg- in Indo-European roots + Greek hodos, way, path) + -ic.]

er·god′i·cal·ly adv.


(Mathematics) maths of or relating to the probability that any state will recur


(ɜrˈgɒd ɪk)

adj. Math., Statistics.
pertaining to the condition that, in an interval of sufficient duration, a system will return to states that are closely similar to previous ones: the basis of statistical methods used in modern dynamics and atomic theory.
[1925–30; erg- + Greek (h)od(ós) way, road + -ic]
er`go•dic′i•ty (-gəˈdɪs ɪ ti) n.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Adj.1.ergodic - positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions
statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
random - lacking any definite plan or order or purpose; governed by or depending on chance; "a random choice"; "bombs fell at random"; "random movements"
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References in periodicals archive ?
The proposed research is an investigation of intermediate chaos in ergodic theory of dynamical systems.
Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, ergodic theory and number theory.
Shannon [1] first proved the AEP for convergence in probability for stationary ergodic information source with a finite alphabet set.
Specifically, the essence of 'adiabatic' is that given the information source is parametrized according to some appropriate scheme, then within continuous 'pieces' of that parametrization, alterations in parameter values occur slowly enough so that the information source X remains as close to stationary and ergodic as necessary in order to implement the specific limit theorems.
In an ergodic forest, while the size, shape and spacing of individual trees may vary, their distribution in any given area is the same as any other area.
capital series) and making sure that after this path has converged to the ergodic set, the predictions of agents are accurate for behavior inside that set.
If [PHI] is ergodic, then the estimator is strongly consistent, when enlarging the window of observation (from Corollary 10.
His thesis examines the paratextual and ergodic elements of Douglas Coupland's novels.
t] in Equation 8 are the ergodic probabilities of being in each of the two states.
If the process is spatially ergodic, then the histogram of the realized noise can be expected to resemble the distribution of the noise process itself.