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 کاملBootstrap Percolation in High Dimensions
In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A ⊂ V (G) is chosen independently at random, with density p, and new vertices are subsequently infected if they have at least r infected neighbours. The set A is said to percolate if eventually all vertices are infected. Our aim is to understand this process on the grid, [n], for arbitrary functions n = n(t)...
متن کاملPolluted Bootstrap Percolation with Threshold Two in All Dimensions
In the polluted bootstrap percolation model, the vertices of a graph are independently declared initially occupied with probability p or closed with probability q. At subsequent steps, a vertex becomes occupied if it is not closed and it has at least r occupied neighbors. On the cubic lattice Z of dimension d ≥ 3 with threshold r = 2, we prove that the final density of occupied sites converges ...
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: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/08-aop433