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Uniform bounds for exponential moment of maximum of a Dyck path


 
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1. Title Title of document Uniform bounds for exponential moment of maximum of a Dyck path
 
2. Creator Author's name, affiliation, country Oleksiy Khorunzhiy; Université de Versailles, France
 
2. Creator Author's name, affiliation, country Jean-François Marckert; CNRS, LabRI, Université de Bordeaux
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Dyck paths; Bernoulli bridge; random matrices
 
3. Subject Subject classification 60C05; 60G70; 60F99
 
4. Description Abstract Let us consider the maximum $M(D)$ of a Dyck path $D$ chosen uniformly in the set of Dyck paths with $2n$ steps. We prove that the exponential moment of $M(D)$ normalized by the square root of $n$ is bounded in the limit of infinite $n$. This uniform bound justifies an assumption used in literature to prove certain estimates of high moments of large random matrices.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-08-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1486
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1486
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
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