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convergence of distributions
Let $p_t$ be a vector of absolute distributions of probabilities in an irreducible aperiodic homogeneous Markov chain with a finite state space. Professor Alladi Ramakrishnan conjectured the following strict inequality for norms of differences $\left\|p_{t+2}-p_{t+1}\right\|<\left\|p_{t+1}-p_t\right\|$. In the paper, a necessary and sufficient condition for the validity of this inequality is proved, which may be useful in investigating the character of convergence of distributions in Markov chains.
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