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Results tagged with ergodic-theory
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user 8135
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
3
votes
2
answers
238
views
Estimate entropy of a binary process in terms of decay of correlations
Suppose $( X_{n} )$ is an ergodic binary process with
$$
\mathbb P(X_{n}=1)= \mathbb P(X_{n}=0)=\frac 12.
$$
Naturally the entropy (rate) $h(X)$ of $X=(X_{n})$ satisfies
$$
h(X)=\lim_{n\to\infty} \f …
- 650
1
vote
Accepted
functions whose average along orbits is zero or a constant
Second part: if your system is nontrivial, and function $f$ is "smooth", than condition
of the form
$$
\lim_{n\to\infty} \frac 1n\sum_{i=0}^{n-1} f(T^i x) =c
$$
for all $\ x$, should imply that
$$
f …
- 650