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Soft edge results for longest increasing paths on the planar lattice


 
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1. Title Title of document Soft edge results for longest increasing paths on the planar lattice
 
2. Creator Author's name, affiliation, country Nicos Georgiou; UW-Madison
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Bernoulli matching model; Discrete TASEP; soft edge; weak law of large numbers; last passage model; increasing paths
 
3. Subject Subject classification 60K35
 
4. Description Abstract For two-dimensional last-passage time models of weakly increasing paths, interesting scaling limits have been proved for points close the axis (the hard edge). For strictly increasing paths of Bernoulli($p$) marked sites, the relevant boundary is the line $y=px$. We call this the soft edge to contrast it with the hard edge. We prove laws of large numbers for the maximal cardinality of a strictly increasing path in the rectangle $[p^{-1}n -xn^a]\times[n]$ as the parameters $a$ and $x$ vary. The results change qualitatively as $a$ passes through the value $1/2$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2010-01-07
 
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/1519
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1519
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
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