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Conditional Limit Theorems for Ordered Random Walks


 
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1. Title Title of document Conditional Limit Theorems for Ordered Random Walks
 
2. Creator Author's name, affiliation, country Denis E Denisov; Cardiff University; United Kingdom
 
2. Creator Author's name, affiliation, country Vitali Wachtel; University of Munich; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Dyson's Brownian Motion, Doob h-transform, Weyl chamber
 
3. Subject Subject classification Primary 60G50; Secondary 60G40, 60F17
 
4. Description Abstract In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a $k$-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the optimal moment assumptions for the construction proposed by Eichelsbacher and Koenig, and generalise the limit theorem for this conditional process.
 
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7. Date (YYYY-MM-DD) 2010-04-08
 
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/752
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-752
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
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