Geodesic
Rare Events and Conditional Events on Random Strings
Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2.

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Some strings -the texts- are assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or under-representation of a word or a set of words. The aim of this paper is twofold. First, a single word is given. One studies the tail distribution of the number of its occurrences. Sharp large deviation estimates are derived. Second, one assumes that a given word is overrepresented. The distribution of a second word is studied; formulae for the expectation and the variance are derived. In both cases, the formulae are accurate and actually computable. These results have applications in computational biology, where a genome is viewed as a text. 
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     author = {R\'egnier, Mireille and Denise, Alain},
     title = {Rare {Events} and {Conditional} {Events} on {Random} {Strings}},
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Régnier, Mireille; Denise, Alain. Rare Events and Conditional Events on Random Strings. Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2. doi : 10.46298/dmtcs.310. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.310/

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