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Soft edge results for longest increasing paths on the planar lattice
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 [bp-1n- xnac]×[n] as the parameters a and x vary. The results change qualitatively as a passes through the value 1/2.
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- Published
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- Published version
Journal
Electronic Communications in ProbabilityISSN
1083-589XPublisher
Institute of Mathematical StatisticsExternal DOI
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15Page range
1-13Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2013-11-08First Compliant Deposit (FCD) Date
2013-11-08Usage metrics
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