A Problem in Last-Passage Percolation
| dc.creator | Kesten, Harry | |
| dc.creator | Sidoravicius, Vladas | |
| dc.date | 2007-06-25 | |
| dc.date.accessioned | 2026-07-07T08:12:13Z | |
| dc.date.available | 2026-07-07T08:12:13Z | |
| dc.description | Let $\{X(v), v \in \Bbb Z^d \times \Bbb Z_+\}$ be an i.i.d. family of random variables such that $P\{X(v)= e^b\}=1-P\{X(v)= 1\} = p$ for some $b>0$. We consider paths $π\subset \Bbb Z^d \times \Bbb Z_+$ starting at the origin and with the last coordinate increasing along the path, and of length $n$. Define for such paths $W(π) = \text{number of vertices $π_i, 1 \le i \le n$, with}X(π_i) = e^b$. Finally let $N_n(\al) = \text{number of paths $π$ of length $n$ starting at $π_0 = \bold 0$ and with $W(π) \ge \al n$.}$ We establish several properties of $\lim_{n \to \infty} [N_n]^{1/n}$. | |
| dc.description | 1 figure | |
| dc.identifier | https://arxiv.org/abs/0706.3626 | |
| dc.identifier | http://arxiv.org/abs/0706.3626 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132379 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | Primary 60K35, secondary 60J15 | |
| dc.title | A Problem in Last-Passage Percolation | |
| dc.type | text |