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- W2952346871 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 $[fl{p^{-1}n -xn^a}]times[n]$ as the parameters $a$ and $x$ vary. The results change qualitatively as $a$ passes through the value 1/2." @default.
- W2952346871 created "2019-06-27" @default.
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- W2952346871 date "2010-03-17" @default.
- W2952346871 modified "2023-09-23" @default.
- W2952346871 title "Soft edge results for longest increasing paths on the planar lattice" @default.
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