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First occurrence of a word among the elements of a finite dictionary in random sequences of letters


 
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1. Title Title of document First occurrence of a word among the elements of a finite dictionary in random sequences of letters
 
2. Creator Author's name, affiliation, country Emilio De Santis; University of Roma "La Sapienza"; Italy
 
2. Creator Author's name, affiliation, country Fabio L. Spizzichino; University of Roma "La Sapienza"; Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Competing words; Sub-words; Renewal Theorem; Ergodic
 
3. Subject Subject classification 60C05; 65C50
 
4. Description Abstract In this paper we study a classical model concerning  occurrence of words in a random sequence of letters from an alphabet. The problem can be studied as a game among $(m+1)$ words: the winning word in this game is the one that occurs first.  We prove that the knowledge of the  first $m$ words results in an advantage in the construction of the last word, as it has been shown in the literature for the cases $m=1$ and $m=2$ [CZ1,CZ2]. The last word can in fact be constructed so that its probability of winning is strictly larger than $1/(m+1)$. For the latter probability we will give an explicit lower bound. Our method is based on rather general  probabilistic arguments that allow us to consider an arbitrary cardinality  for the alphabet, an arbitrary value for $m$ and different mechanisms generating the random sequence of letters.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) PRIN 2009Y3PX3X_004 Applicazioni fisiche di campi aleatori; 2009 Research Project "Modelli e Algoritmi Stocastici: Convergenza e Ottimizzazione" University "La Sapienza", Rome
 
7. Date (YYYY-MM-DD) 2012-03-20
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1878
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1878
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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