Slightly subcritical hypercube percolation
نویسندگان
چکیده
منابع مشابه
On acoustic cavitation of slightly subcritical bubbles
The classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies a critical radius which separates quasistatically stable bubbles from those which would cavitate. In this work, we analyze the cavitation threshold for radia...
متن کاملLargest cluster in subcritical percolation
The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size N is investigated (below the upper critical dimension, presumably d(c)=6). It is argued that as N-->infinity the cumulative distribution function converges to the Fisher-Tippett (or Gumbel) distribution e(-e(-z)) in a certain weak sense (when suitably normalized). The mea...
متن کاملSaturation in the Hypercube and Bootstrap Percolation
Let Qd denote the hypercube of dimension d. Given d ≥ m, a spanning subgraph G of Qd is said to be (Qd, Qm)-saturated if it does not contain Qm as a subgraph but adding any edge of E(Qd) \E(G) creates a copy of Qm in G. Answering a question of Johnson and Pinto [27], we show that for every fixed m ≥ 2 the minimum number of edges in a (Qd, Qm)-saturated graph is Θ(2 d). We also study weak satura...
متن کاملMajority Bootstrap Percolation on the Hypercube
In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain infected forever. Percolation occurs if eventually every vertex is infected. The elements of the set of initially infected vertices, A ⊂ V (G), are normally...
متن کاملSubcritical U-bootstrap Percolation Models Have Non-trivial Phase Transitions
We prove that there exist natural generalizations of the classical bootstrap percolation model on Z that have non-trivial critical probabilities, and moreover we characterize all homogeneous, local, monotone models with this property. Van Enter [28] (in the case d = r = 2) and Schonmann [25] (for all d > r > 2) proved that r-neighbour bootstrap percolation models have trivial critical probabili...
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: Random Structures & Algorithms
سال: 2019
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20853