Let 02 the value a with probability p or the value b with probability 1−p. For all u,v∈ℤ2, let T(u,v) denote the first passage time between u and v. We show that there are points x∈ℝ2 such that the “time constant” in the direction of x, namely, lim n→∞n−1Ep[T(0,nx)], is not a three times differentiable function of p.
Publié le : 2006-03-14
Classification:
First passage percolation,
shape theory,
the right-hand edge,
nondifferentiability of time constants,
60K35
@article{1147179983,
author = {Yukich, J. E. and Zhang, Yu},
title = {Singularity points for first passage percolation},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 577-592},
language = {en},
url = {http://dml.mathdoc.fr/item/1147179983}
}
Yukich, J. E.; Zhang, Yu. Singularity points for first passage percolation. Ann. Probab., Tome 34 (2006) no. 1, pp. 577-592. http://gdmltest.u-ga.fr/item/1147179983/