It is the ergodicity
associated to the candidate generation distribution (its "offspring operator" in the terminology of EA's).
In part this is a signal that ergodicity
(and convergence, more generally) is itself a problematic concept, a topic that would take me somewhat afield of my current program.
is tacitly assumed by most authors doing empirical research involving equity and bond prices because they estimate, say, the average price in some future potential state of the economy, by the using the average of past prices (which reflect just one state of the world at each point observed over time).
According to that, many properties of chaotic systems such as: ergodicity
, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems .
ij] = 1 for 1 [less than or equal to] i [less than or equal to] N), and due to the ergodicity
assumption it is irreducible.
At the glass transition point, the phase space is decomposed into a set of mutually independent structural elements (traps), which is revealed as ergodicity
The concepts of equilibrium, disequilibrium, dynamic instability and ergodicity
, structural instability, and rationality and causality are accentuated.
surveys progress on the quantum unique ergodicity
conjecture concerning the distribution of large frequency eigenfunctions of the Laplacian on a negatively curved manifold.
properties of the chain we can estimate statistical characteristics of [LAMBDA].
This is followed by a chapter on log Sobolev inequalities with an application to a strong ergodicity
theorem for Kolmogorov diffusion processes.
Some sections from the 1994 first edition have been removed for this second, and new sections added on capacities and Sobolev type inequalities, irreducible recurrence and ergodicity
, recurrence and Poincare type inequalities, and Donsker-Varadhan type large deviation principles.
The characteristics of the chaotic maps have attracted the attention of cryptographers since it has many fundamental properties such as ergodicity
, sensitivity to initial condition and system parameter, and mixing property, etc [15-16].