A problem in last-passage percolation

Kesten, Harry; Sidoravicius, Vladas

Braz. J. Probab. Stat., Tome 24 (2010) no. 1, p. 300-320 / Harvested from Project Euclid

Résumé

Let {X(v), v∈ℤ^d×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⊂ℤ^d×ℤ₊ starting at the origin and with the last coordinate increasing along the path, and of length n. Define for such paths W(π)= number of vertices π_i, 1≤i≤n, with X(π_i)=e^b. Finally, let N_n(α)= number of paths π of length n starting at π₀=0 and with W(π)≥αn. We establish several properties of lim_n→∞[N_n]^1/n.

Publié le : 2010-07-15
Classification: Oriented first passage percolation, directed polymer, free energy

@article{1271770273,
     author = {Kesten, Harry and Sidoravicius, Vladas},
     title = {A problem in last-passage percolation},
     journal = {Braz. J. Probab. Stat.},
     volume = {24},
     number = {1},
     year = {2010},
     pages = { 300-320},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1271770273}
}

Kesten, Harry; Sidoravicius, Vladas. A problem in last-passage percolation. Braz. J. Probab. Stat., Tome 24 (2010) no. 1, pp.  300-320. http://gdmltest.u-ga.fr/item/1271770273/