A Problem in Last-Passage Percolation

dc.creatorKesten, Harry
dc.creatorSidoravicius, Vladas
dc.date2007-06-25
dc.date.accessioned2026-07-07T08:12:13Z
dc.date.available2026-07-07T08:12:13Z
dc.descriptionLet $\{X(v), v \in \Bbb Z^d \times \Bbb Z_+\}$ 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.description1 figure
dc.identifierhttps://arxiv.org/abs/0706.3626
dc.identifierhttp://arxiv.org/abs/0706.3626
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132379
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectPrimary 60K35, secondary 60J15
dc.titleA Problem in Last-Passage Percolation
dc.typetext

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