Recent advances in percolation theory and its applications

AA Saberi - Physics Reports, 2015‏ - Elsevier
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase
transitions signaled by the emergence of a giant connected component. Despite its very …

[ספר][B] Dynamical heterogeneities in glasses, colloids, and granular media

L Berthier, G Biroli, JP Bouchaud, L Cipelletti… - 2011‏ - books.google.com
Most of the solid materials we use in everyday life, from plastics to cosmetic gels exist under
a non-crystalline, amorphous form: they are glasses. Yet, we are still seeking a fundamental …

Glassy dynamics of kinetically constrained models

F Ritort, P Sollich - Advances in physics, 2003‏ - Taylor & Francis
We review the use of kinetically constrained models (KCMs) for the study of dynamics in
glassy systems. The characteristic feature of KCMs is that they have trivial, often non …

Sharp metastability threshold for two-dimensional bootstrap percolation

AE Holroyd - Probability theory and related fields, 2003‏ - Springer
In the bootstrap percolation model, sites in an L by L square are initially independently
declared active with probability p. At each time step, an inactive site becomes active if at …

The sharp threshold for bootstrap percolation in all dimensions

J Balogh, B Bollobás, H Duminil-Copin… - Transactions of the …, 2012‏ - ams.org
In $ r $-neighbour bootstrap percolation on a graph $ G $, a (typically random) set $ A $ of
initially 'infected'vertices spreads by infecting (at each time step) vertices with at least $ r …

Bootstrap percolation on the random graph

S Janson, T Łuczak, T Turova, T Vallier - 2012‏ - projecteuclid.org
Bootstrap percolation on the random graph G_n,p is a process of spread of “activation” on a
given realization of the graph with a given number of initially active nodes. At each step …

Bootstrap percolation on the random regular graph

J Balogh, BG Pittel - Random Structures & Algorithms, 2007‏ - Wiley Online Library
The k‐parameter bootstrap percolation on a graph is a model of an interacting particle
system, which can also be viewed as a variant of a cellular automaton growth process with …

Irreversible conversion of graphs

CC Centeno, MC Dourado, LD Penso… - Theoretical Computer …, 2011‏ - Elsevier
Given a graph G, a function f: V (G)→ Z, and an initial 0/1-vertex-labelling c 1: V (G)→{0, 1},
we study an iterative 0/1-vertex-labelling process on G where in each round every vertex v …

Bootstrap percolation on the hypercube

J Balogh, B Bollobás - Probability Theory and Related Fields, 2006‏ - Springer
In the bootstrap percolation on the n-dimensional hypercube, in the initial position each of
the 2 n sites is occupied with probability p and empty with probability 1− p, independently of …

Kinetically constrained models

JP Garrahan, P Sollich, C Toninelli - … heterogeneities in glasses …, 2011‏ - books.google.com
In this chapter we summarize recent developments in the study of kinetically constrained
models (KCMs) as models for glass formers. After recalling the definition of the KCMs that …