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  1. Probability Theory and Related Fields
  2. Probability Theory and Related Fields : Volume 134
  3. Probability Theory and Related Fields : Volume 134, Issue 4, April 2006
  4. Bootstrap percolation on the hypercube
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Probability Theory and Related Fields : Volume 165
Probability Theory and Related Fields : Volume 164
Probability Theory and Related Fields : Volume 163
Probability Theory and Related Fields : Volume 162
Probability Theory and Related Fields : Volume 161
Probability Theory and Related Fields : Volume 160
Probability Theory and Related Fields : Volume 159
Probability Theory and Related Fields : Volume 158
Probability Theory and Related Fields : Volume 157
Probability Theory and Related Fields : Volume 156
Probability Theory and Related Fields : Volume 155
Probability Theory and Related Fields : Volume 154
Probability Theory and Related Fields : Volume 153
Probability Theory and Related Fields : Volume 152
Probability Theory and Related Fields : Volume 151
Probability Theory and Related Fields : Volume 150
Probability Theory and Related Fields : Volume 149
Probability Theory and Related Fields : Volume 148
Probability Theory and Related Fields : Volume 147
Probability Theory and Related Fields : Volume 146
Probability Theory and Related Fields : Volume 145
Probability Theory and Related Fields : Volume 144
Probability Theory and Related Fields : Volume 143
Probability Theory and Related Fields : Volume 142
Probability Theory and Related Fields : Volume 141
Probability Theory and Related Fields : Volume 140
Probability Theory and Related Fields : Volume 139
Probability Theory and Related Fields : Volume 138
Probability Theory and Related Fields : Volume 137
Probability Theory and Related Fields : Volume 136
Probability Theory and Related Fields : Volume 135
Probability Theory and Related Fields : Volume 134
Probability Theory and Related Fields : Volume 134, Issue 4, April 2006
Sharp adaptive estimation of quadratic functionals
On symmetric random walks with random conductances on ℤd
Classification and decomposition of Quantum Markov Semigroups
Bootstrap percolation on the hypercube
Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian
Probability Theory and Related Fields : Volume 134, Issue 3, March 2006
Probability Theory and Related Fields : Volume 134, Issue 2, February 2006
Probability Theory and Related Fields : Volume 134, Issue 1, January 2006
Probability Theory and Related Fields : Volume 133
Probability Theory and Related Fields : Volume 132
Probability Theory and Related Fields : Volume 131
Probability Theory and Related Fields : Volume 130
Probability Theory and Related Fields : Volume 129
Probability Theory and Related Fields : Volume 128
Probability Theory and Related Fields : Volume 127
Probability Theory and Related Fields : Volume 126
Probability Theory and Related Fields : Volume 125
Probability Theory and Related Fields : Volume 124
Probability Theory and Related Fields : Volume 123
Probability Theory and Related Fields : Volume 122
Probability Theory and Related Fields : Volume 121
Probability Theory and Related Fields : Volume 120
Probability Theory and Related Fields : Volume 119
Probability Theory and Related Fields : Volume 118
Probability Theory and Related Fields : Volume 117
Probability Theory and Related Fields : Volume 116
Probability Theory and Related Fields : Volume 115
Probability Theory and Related Fields : Volume 114
Probability Theory and Related Fields : Volume 113
Probability Theory and Related Fields : Volume 112
Probability Theory and Related Fields : Volume 111
Probability Theory and Related Fields : Volume 110
Probability Theory and Related Fields : Volume 109
Probability Theory and Related Fields : Volume 108
Probability Theory and Related Fields : Volume 107

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Bootstrap percolation on the hypercube

Content Provider Springer Nature Link
Author Balogh, József Bollobás, Béla
Copyright Year 2005
Abstract In the bootstrap percolation on the n-dimensional hypercube, in the initial position each of the 2n sites is occupied with probability p and empty with probability 1−p, independently of the state of the other sites. Every occupied site remains occupied for ever, while an empty site becomes occupied if at least two of its neighbours are occupied. If at the end of the process every site is occupied, we say that the (initial) position spans the hypercube. We shall show that there are constants c1,c2>0 such that for the probability of spanning tends to 1 as n→∞, while for the probability tends to 0. Furthermore, we shall show that for each n the transition has a sharp threshold function.
Starting Page 624
Ending Page 648
Page Count 25
File Format PDF
ISSN 01788051
Journal Probability Theory and Related Fields
Volume Number 134
Issue Number 4
e-ISSN 14322064
Language English
Publisher Springer-Verlag
Publisher Date 2005-07-14
Publisher Place Berlin/Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Operations Research/Decision Theory Quantitative Finance Probability Theory and Stochastic Processes Mathematical Biology in General Mathematical and Computational Physics Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type Text
Resource Type Article
Subject Statistics and Probability Analysis Statistics, Probability and Uncertainty
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