| Título: | Soft edge results for longest increasing paths on the planar lattice |
| Autores: | Georgiou, Nicos; UW-Madison |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Bernoulli matching model; Discrete TASEP; soft edge; weak law of large numbers; last passage model; increasing paths 60K35 |
| Descripción: | 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 $1/2$. |
| Idioma: | No aplica |
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