What is the distribution of the distance between a specific word in a Text which is generated by a markov process? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T07:20:14Z http://mathoverflow.net/feeds/question/111033 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111033/what-is-the-distribution-of-the-distance-between-a-specific-word-in-a-text-which What is the distribution of the distance between a specific word in a Text which is generated by a markov process? gstar2002 2012-10-29T22:10:40Z 2012-10-29T23:23:30Z <p>What is the distribution of the distance between a specific word in a Text which is generated by a markov process?</p> <p>For example for a text which is generated by a multinomial distribution over words, this distribution of distance will be a Geometric distribution. Thanks.</p> http://mathoverflow.net/questions/111033/what-is-the-distribution-of-the-distance-between-a-specific-word-in-a-text-which/111038#111038 Answer by Omer for What is the distribution of the distance between a specific word in a Text which is generated by a markov process? Omer 2012-10-29T23:23:30Z 2012-10-29T23:23:30Z <p>With infinitely many states, any distribution is possible, as demonstrated by a Markov chains on \$N\$ which jump from \$n\$ only to \$n+1\$ or \$0\$.</p> <p>If the Markov chain is has finitely many states, or is reversible, many distributions are possible, and there is no complete characterization of which distributions can or cannot appear. In the former case you must have exponential tail. In the latter, there are also some results in certain cases, see e.g. this paper: <a href="http://arxiv.org/abs/1009.1438" rel="nofollow">http://arxiv.org/abs/1009.1438</a>.</p>