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Movie Name: Mrugam. Director: Sameer. Star Cast: Kishore, Shasi, Leena. Year: 2010. Language: Telugu. Size: 3.09 GB.
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[**Proof of Theorem \[thm:equidistribution\]**]{}
Let ${\mathcal{I}}$ be the collection of infinite words which have period less than $\ell$ under $Z$. We observe that, under $Z$, the set of all words of length $n$ has probability $(2d)^n/n!\to \exp(-(1+\rho)d)$ for large $n$; this follows easily from the [@angelosante Theorem 1] in the special case $d=1$. It follows that the limit in the claim of the theorem is the same as the limit of the set ${\mathcal{I}}$.
The last claim follows immediately, since for each $w$ in ${\mathcal{I}}$ there exists a constant $c>0$ such that $\prob(Z_{n+1}=w|Z_n=w)\le c$ for all $n$. To see this, note that for any two configurations $Z,Z'$ on the same site and with at least one coordinate different, $\prob(Z_{n+1}=w|Z_n=w)$ is non-decreasing in $n$ since in this case $\prob(Z'_{n+1}=w|Z'_n=w)$ decreases by at least a factor of $n 0b46394aab
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