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Soft edge results for longest increasing paths on the planar lattice

journal contribution
posted on 2023-06-08, 16:17 authored by Nicos GeorgiouNicos Georgiou
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Electronic Communications in Probability

ISSN

1083-589X

Publisher

Institute of Mathematical Statistics

Volume

15

Page range

1-13

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-11-08

First Compliant Deposit (FCD) Date

2013-11-08

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