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Recent advances in percolation theory and its applications
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 …
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 …
a non-crystalline, amorphous form: they are glasses. Yet, we are still seeking a fundamental …
Glassy dynamics of kinetically constrained models
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 …
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 …
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
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 …
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 …
given realization of the graph with a given number of initially active nodes. At each step …
Bootstrap percolation on the random regular graph
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 …
system, which can also be viewed as a variant of a cellular automaton growth process with …
Irreversible conversion of graphs
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 …
we study an iterative 0/1-vertex-labelling process on G where in each round every vertex v …
Bootstrap percolation on the hypercube
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 …
the 2 n sites is occupied with probability p and empty with probability 1− p, independently of …
Kinetically constrained models
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 …
models (KCMs) as models for glass formers. After recalling the definition of the KCMs that …