Subcritical $\mathcal {U}$-bootstrap percolation models have non-trivial phase transitions
نویسندگان
چکیده
منابع مشابه
Subcritical 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 کاملBootstrap percolation on homogeneous trees has 2 phase transitions
We study the threshold θ bootstrap percolation model on the homogeneous tree with degree b+ 1, 2 ≤ θ ≤ b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call pf , such that a) for p > pf , the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < pf , then for almost every initial configuration,...
متن کاملBehavioral Intervention and Non-Uniform Bootstrap Percolation
Bootstrap percolation is an often used model to study the spread of diseases, rumors, and information on sparse random graphs. The percolation process demonstrates a critical value such that the graph is either almost completely affected or almost completely unaffected based on the initial seed being larger or smaller than the critical value. In this paper, we consider behavioral interventions,...
متن کاملExistence of non-trivial solutions for fractional Schrödinger-Poisson systems with subcritical growth
In this paper, we are concerned with the following fractional Schrödinger-Poisson system: (−∆s)u + u + λφu = µf(u) +|u|p−2|u|, x ∈R3 (−∆t)φ = u2, x ∈R3 where λ,µ are two parameters, s,t ∈ (0,1] ,2t + 4s > 3 ,1 < p ≤ 2∗ s and f : R → R is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with ...
متن کاملPhase Transitions in a Nonequilibrium Percolation Model
We investigate the percolation properties of a two–state (occupied – empty) cellular automaton, where at each time step a cluster of occupied sites is removed and the same number of randomly chosen empty sites are occupied again. We find a finite region of critical behavior, formation of synchronized stripes, additional phase transitions, as well as violation of the usual finite– size scaling a...
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: Transactions of the American Mathematical Society
سال: 2016
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6586