Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Fey, Anne"'
Autor:
Fey, Anne, Meester, Ronald
We discuss various critical densities in sandpile models. The stationary density is the average expected height in the stationary state of a finite-volume model; the transition density is the critical point in the infinite-volume counterpart. These t
Externí odkaz:
http://arxiv.org/abs/1211.4760
Autor:
van Enter, Aernout, Fey, Anne
In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability threshold for a fairly general class of models. In our proofs we use an adaptation of the technique
Externí odkaz:
http://arxiv.org/abs/1110.0733
Autor:
Fey, Anne, Liu, Haiyan
We present limiting shape results for a non-abelian variant of the abelian sandpile growth model (ASGM), some of which have no parallel in the ASGM. One of our limiting shapes is an octagon. In our model, mass spreads from the origin by the toppling
Externí odkaz:
http://arxiv.org/abs/1006.4928
Publikováno v:
Phys. Rev. E 82, 031121 (2010)
A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model should be e
Externí odkaz:
http://arxiv.org/abs/1001.3401
Publikováno v:
Physical Review Letters, 104:145703, 2010
A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals the threshold density of the fixed-energy sandpile.
Externí odkaz:
http://arxiv.org/abs/0912.3206
Publikováno v:
J. Stat. Phys. 138, 143--159 (2010)
We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Z^d. Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant b
Externí odkaz:
http://arxiv.org/abs/0901.3805
Publikováno v:
Electronic Journal of Probability 14 (2009), 895-911
We show that Zhang's sandpile model (N,[a,b]) on N sites and with uniform additions on [a,b] has a unique stationary measure for all 0 <= a < b <= 1. This generalizes earlier results where this was shown in some special cases. We define the infinite
Externí odkaz:
http://arxiv.org/abs/0809.2913
Publikováno v:
Advances in Applied Probability 40 nr. 4 (2008), 1048-1071
We study sample covariance matrices of the form $W=\frac 1n C C^T$, where $C$ is a $k\times n$ matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the entries of $C$ are independent and identically dist
Externí odkaz:
http://arxiv.org/abs/0712.3650
Publikováno v:
Annals of Probability 2009, Vol. 37, No. 2, 654-675
We study the sandpile model in infinite volume on $\mathbb{Z}^d$. In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure $\mu$, are $\mu$-almost surely stabilizable. We prove t
Externí odkaz:
http://arxiv.org/abs/0710.0939
Autor:
Fey, Anne, Redig, Frank
Publikováno v:
Journal of Statistical Physics (2008) 130: 579-597
We study the rotor router model and two deterministic sandpile models. For the rotor router model in $\mathbb{Z}^d$, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension
Externí odkaz:
http://arxiv.org/abs/math/0702450