منابع مشابه
Bootstrap Percolation in Three Dimensions
Abstract. By bootstrap percolation we mean the following deterministic process on a graph G. Given a set A of vertices ‘infected’ at time 0, new vertices are subsequently infected, at each time step, if they have at least r ∈ N previously infected neighbours. When the set A is chosen at random, the main aim is to determine the critical probability pc(G, r) at which percolation (infection of the...
متن کاملPolluted Bootstrap Percolation in Three Dimensions
In the polluted bootstrap percolation model, vertices of the cubic lattice Z are independently declared initially occupied with probability p or closed with probability q. Under the standard (respectively, modified) bootstrap rule, a vertex becomes occupied at a subsequent step if it is not closed and it has at least 3 occupied neighbors (respectively, an occupied neighbor in each coordinate). ...
متن کاملSemi-oriented bootstrap percolation in three dimensions
We consider the critical system size of a three dimensional semi-oriented bootstrap percolation model, constricted to a 3D cube wrapped to a torus, i.e. with periodical boundary conditions. We point out a possible form of the critical droplets for this model: occupied squares in a plane perpendicular to the primary direction of the dynamics behave as growing seeds when they are suuciently large...
متن کاملBond and site percolation in three dimensions.
We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be p(c)(bond)=0.24881182(10) and p(c)(site)=0.3116077(2). By performing extensive simulations at these estimated critical points, we then estimate the critical exponents 1/ν=1.1410(15), β/ν=0.47705(15), the leading correction exponent y(i)=-1.2(2),...
متن کاملGaussian model of explosive percolation in three and higher dimensions.
The Gaussian model of discontinuous percolation, recently introduced by Araújo and Herrmann [Phys. Rev. Lett. 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple cubic lattice, in the thermodynamic limit we report a finite jump of the order parameter J=0.415±0.005. The largest cluster at the threshold is compact, but its ex...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2014
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-014-0600-x