Discrete Mathematics & Theoretical Computer Science
| author: | Mireille Régnier and Alain Denise |
|---|---|
| title: | Rare Events and Conditional Events on Random Strings |
| keywords: | large deviations, combinatorics, generating fumctions, words, genome, computable closed formulae. |
| abstract: | 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.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |
| reference: | Mireille Régnier and Alain Denise (2004), Rare Events and Conditional Events on Random Strings, Discrete Mathematics and Theoretical Computer Science 6, pp. 191-214 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dm060203.ps.gz (95 K) |
| ps-source: | dm060203.ps (261 K) |
| pdf-source: | dm060203.pdf (182 K) |
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