The Erdos-Renyi Law in Distribution, for Coin Tossing and Sequence Matching

Arratia, Richard; Gordon, Louis; Waterman, Michael S.

doi:10.1214/aos/1176347615

Cited by 140 publications

(105 citation statements)

References 12 publications

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“…Among the many papers on that subject we refer to the theoretical papers [5], [6], [9], and [19] and the more applied papers [13] and [20]. The result that comes closest to Theorem 1 is the one obtained by Dembo et al [9, Theorem 1] about gapless, local alignment using a general score function.…”

Section: Local Stacks and Local Alignmentmentioning

confidence: 85%

Asymptotics for local maximal stack scores with general loop penalty function

Hansen

2007

Adv. Appl. Probab.

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A stack is a structural unit in an RNA structure that is formed by pairs of hydrogen bonded nucleotides. Paired nucleotides are scored according to their ability to hydrogen bond. We consider stack/hairpin-loop structures for a sequence of independent and identically distributed random variables with values in a finite alphabet, and we show how to obtain an asymptotic Poisson distribution of the number of stack/hairpin-loop structures with a score exceeding a high threshold, given that we count in a proper, declumped way. From this result we obtain an asymptotic Gumbel distribution of the maximal stack score. We also provide examples focusing on the computation of constants that enter in the asymptotic distributions. Finally, we discuss the close relation to existing results for local alignment.

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Section: Local Stacks and Local Alignmentmentioning

confidence: 85%

Asymptotics for local maximal stack scores with general loop penalty function

Hansen

2007

Adv. Appl. Probab.

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“…Waterman (Arratia et al, 1986;Arratia et al, 1990) and Karlin and Altschul (Karlin & Altschul, 1990;Karlin et al, 1991) demonstrated that local similarity scores are expected to follow the extremevalue distribution. Waterman presents an intuitive argument in (Waterman, 1995), where, referring to Erdös and Renyí, he points out that the expected number of runs of heads of length l in n coin tosses is E(l) ∼ = np l , where p is the probability of heads (Fig.…”

Section: Statistics Of Alignments Without Gapsmentioning

confidence: 99%

Statistical Significance in Biological Sequence Comparison

Pearson

Wood

2007

Handbook of Statistical Genetics

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“…where g(z,h) = h -(x mod h) if (x mod h) : 0 and g(z,h) = h if (x mod h) = 0 (see [12], page 513 or [22], page 171, Theorem 6). Thus, by adopting the argument above for the lattice case, one obtains …”

Section: An(an L A)mentioning

confidence: 99%

Large Deviations and Applications: The Finite Dimensional Case

Dembo¹,

Zeitouni²

1991

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Preface and WarningThese notes, which form the first chapter of a forthcoming book, are intended to serve as lecture notes on the topic of large deviations and applications for students whose background and interests are in applications which involve finite dimensional spaces. Although narrow in their scope, these notes present a good deal of the methods available for more general situations. A glaring omission is the method of sub-additivity, which will be discussed in another chapter in the book. Another deficiency of these notes is the sketchy bibliography and historical. We hope to correct this in the book.

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The Erdos-Renyi Law in Distribution, for Coin Tossing and Sequence Matching

Cited by 140 publications

References 12 publications

Asymptotics for local maximal stack scores with general loop penalty function

Asymptotics for local maximal stack scores with general loop penalty function

Statistical Significance in Biological Sequence Comparison

Large Deviations and Applications: The Finite Dimensional Case

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