$A simple branching process approach to the phase transition in $G_{n,p}$$

A simple branching process approach to the phase transition in $G_{n,p}$

It is well known that the branching process approach to the study of the random graph $G_{n,p}$ gives a very simple way of understanding the size of the giant component when it is fairly large (of order $\Theta(n)$). Here we show that a variant of this approach works all the way down to the phase tr...

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Bibliografiske detaljer
Main Authors:	Bollobas, B, Riordan, O
Format:	Journal article
Sprog:	English
Udgivet:	2012

Lignende værker

The cut metric, random graphs, and branching processes
af: Bollobas, B, et al.
Udgivet: (2009)

The phase transition in inhomogeneous random graphs
af: Bollobas, B, et al.
Udgivet: (2005)

The phase transition in the uniformly grown random graph has infinite order
af: Bollobas, B, et al.
Udgivet: (2005)

An old approach to the giant component problem
af: Bollobas, B, et al.
Udgivet: (2012)

Achlioptas process phase transitions are continuous
af: Riordan, O, et al.
Udgivet: (2011)

The k-core and branching processes
af: Riordan, O
Udgivet: (2005)

Sesqui-type branching processes
af: Janson, S, et al.
Udgivet: (2018)

A note on the Harris-Kesten Theorem
af: Bollobas, B, et al.
Udgivet: (2005)

A short proof of the Harris-Kesten Theorem
af: Bollobas, B, et al.
Udgivet: (2004)

Asymptotic normality of the size of the giant component in a random hypergraph
af: Bollobás, B, et al.
Udgivet: (2012)

Asymptotic normality of the size of the giant component in a random hypergraph
af: Bollobas, B, et al.
Udgivet: (2011)

Asymptotic normality of the size of the giant component via a random walk
af: Bollobas, B, et al.
Udgivet: (2010)

Asymptotic normality of the size of the giant component via a random walk
af: Bollobás, B, et al.
Udgivet: (2011)

The phase transition in the configuration model
af: Riordan, O
Udgivet: (2011)

Percolation on self-dual polygon configurations
af: Bollobas, B, et al.
Udgivet: (2010)

Slow emergence of the giant component in the growing m-out graph
af: Bollobas, B, et al.
Udgivet: (2005)

Clique percolation
af: Bollobas, B, et al.
Udgivet: (2008)

The critical probability for random Voronoi percolation in the plane is 1/2
af: Bollobas, B, et al.
Udgivet: (2004)

Sharp thresholds and percolation in the plane
af: Bollobas, B, et al.
Udgivet: (2004)

Exploring hypergraphs with martingales
af: Bollobás, B, et al.
Udgivet: (2017)

Metrics for sparse graphs
af: Bollobas, B, et al.
Udgivet: (2007)

Percolation on dual lattices with k-fold symmetry
af: Bollobas, B, et al.
Udgivet: (2006)

Counting dense connected hypergraphs via the probabilistic method
af: Bollobás, B, et al.
Udgivet: (2018)

Sparse graphs: metrics and random models
af: Bollobas, B, et al.
Udgivet: (2008)

Percolation.
af: Bollobás, B, et al.
Udgivet: (2006)

Percolation on random Johnson-Mehl tessellations and related models (vol 140, pg 319, 2008)
af: Bollobas, B, et al.
Udgivet: (2010)

Erratum: Percolation on random Johnson-Mehl tessellations and related models
af: Bollobas, B, et al.
Udgivet: (2009)

Percolation on random Johnson-Mehl tessellations and related models
af: Bollobas, B, et al.
Udgivet: (2006)

On covering by translates of a set
af: Bollobas, B, et al.
Udgivet: (2009)

Sparse random graphs with clustering
af: Bollobas, B, et al.
Udgivet: (2008)

Line-of-sight percolation
af: Bollobas, B, et al.
Udgivet: (2007)

Monotone graph limits and quasimonotone graphs
af: Bollobas, B, et al.
Udgivet: (2011)

Spread-out percolation in R^d
af: Bollobas, B, et al.
Udgivet: (2005)

Subcritical $ \mathcal{U}$-bootstrap percolation models have non-trivial phase transitions
af: Balister, P, et al.
Udgivet: (2016)

Simple Fermionic Model of Deconfined Phases and Phase Transitions
af: F. F. Assaad, et al.
Udgivet: (2016-12-01)

The consequences of Zipf's law for syntax and symbolic reference.
af: i Cancho, R, et al.
Udgivet: (2005)

Description of two species of early branching dinoflagellates, Psammosa pacifica n. g., n. sp. and P. atlantica n. sp.
af: Noriko Okamoto, et al.
Udgivet: (2012-01-01)

On the maximum running time in graph bootstrap percolation
af: Bollobás, B, et al.
Udgivet: (2017)

Linear algebra and bootstrap percolation
af: Balogh, J, et al.
Udgivet: (2011)

The threshold for jigsaw percolation on random graphs
af: Bollobás, B, et al.
Udgivet: (2017)