DOI: 10.1016/s0304-4149(02)00124-2. The threshold regime of finite volume bootstrap percolation

The threshold regime of finite volume bootstrap percolation

10.1016/s0304-4149(02)00124-2

Crossref journal-article

Elsevier BV

Stochastic Processes and their Applications (78)

Bibliography

Cerf, R., & Manzo, F. (2002). The threshold regime of finite volume bootstrap percolation. Stochastic Processes and Their Applications, 101(1), 69â82.

Authors 2

R. Cerf (first)
F. Manzo (additional)

References 21 Referenced 80

10.1016/0378-4371(91)90295-N / Physica A / Bootstrap percolation by Adler (1991)
10.1088/0305-4470/21/6/015 / J. Phys. A / Diffusion percolation: I. Infinite time limit and bootstrap percolation by Adler (1988)
10.1088/0305-4470/22/7/008 / J. Phys. A / Comparison of bootstrap percolation models by Adler (1989)
10.1007/BF01314923 / J. Statist. Phys. / Finite-size effects for some bootstrap percolation models by Adler (1990)
10.1088/0305-4470/21/19/017 / J. Phys. A / Metastability effects in bootstrap percolation by Aizenman (1988)
10.1088/0022-3719/17/14/001 / J. Phys. C by Branco (1984)
10.1088/0022-3719/19/12/006 / J. Phys. C by Branco (1986)
10.1214/aop/1022874817 / Ann. Probab. / Finite size scaling in three-dimensional bootstrap percolation by Cerf (1999)
10.1088/0022-3719/12/1/008 / J. Phys. C / Bootstrap percolation on a Bethe lattice by Chalupa (1979)
10.1007/s004400050079 / Probab. Theory Related Fields / A nucleation-and-growth model by Dehghanpour (1997)
10.1007/BF01019705 / J. Statist. Phys. / Proof of Straley's argument for bootstrap percolation by van Enter (1987)
10.1007/BF01020891 / J. Statist. Phys. / Addendum: finite-size effects for some bootstrap percolation models by van Enter (1991)
{'key': '10.1016/S0304-4149(02)00124-2_BIB13', 'series-title': 'Percolation', 'author': 'Grimmett', 'year': '1999'} / Percolation by Grimmett (1999)
10.1088/0022-3719/18/9/008 / J. Phys. C by Khan (1985)
{'issue': '4', 'key': '10.1016/S0304-4149(02)00124-2_BIB15', 'first-page': '549', 'article-title': 'Relaxation patterns for competing metastable states: a nucleation and growth model', 'volume': '4', 'author': 'Manzo', 'year': '1998', 'journal-title': 'Markov Process. Related Fields'} / Markov Process. Related Fields / Relaxation patterns for competing metastable states: a nucleation and growth model by Manzo (1998)
10.1016/0304-4149(94)00061-W / Stochastic Process. Appl. / Critical length for semi-oriented bootstrap percolation by Mountford (1995)
10.1007/BF01026574 / J. Statist. Phys. / Critical Points of two-dimensional bootstrap percolation-like cellular automata by Schonmann (1990)
10.1016/0378-4371(90)90280-6 / Phys. A / Finite size scaling behavior of a biased majority rule cellular automaton by Schonmann (1990)
10.1214/aop/1176989923 / Ann. Probab. / On the behavior of some cellular automata related to bootstrap percolation by Schonmann (1992)
10.1016/0167-2789(84)90253-7 / Phys. D / Simulating physics with cellular automata by Vichniac (1984)
10.1103/RevModPhys.55.601 / Rev. Modern Phys. / Statistical mechanics of cellular automata by Wolfram (1983)

Dates

Type	When
Created	22 years, 10 months ago (Oct. 14, 2002, 5:51 p.m.)
Deposited	6 years, 4 months ago (April 13, 2019, 1:55 p.m.)
Indexed	2 weeks, 3 days ago (Aug. 6, 2025, 10 a.m.)
Issued	22 years, 11 months ago (Sept. 1, 2002)
Published	22 years, 11 months ago (Sept. 1, 2002)
Published Print	22 years, 11 months ago (Sept. 1, 2002)

Funders 0

None

BibTeX

@article{Cerf_2002, title={The threshold regime of finite volume bootstrap percolation}, volume={101}, ISSN={0304-4149}, url={http://dx.doi.org/10.1016/s0304-4149(02)00124-2}, DOI={10.1016/s0304-4149(02)00124-2}, number={1}, journal={Stochastic Processes and their Applications}, publisher={Elsevier BV}, author={Cerf, R. and Manzo, F.}, year={2002}, month=sep, pages={69–82} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        6
      ]
    ],
    "date-time": "2025-08-06T14:00:52Z",
    "timestamp": 1754488852758
  },
  "reference-count": 21,
  "publisher": "Elsevier BV",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2002,
            9,
            1
          ]
        ],
        "date-time": "2002-09-01T00:00:00Z",
        "timestamp": 1030838400000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://www.elsevier.com/tdm/userlicense/1.0/"
    },
    {
      "start": {
        "date-parts": [
          [
            2013,
            7,
            17
          ]
        ],
        "date-time": "2013-07-17T00:00:00Z",
        "timestamp": 1374019200000
      },
      "content-version": "vor",
      "delay-in-days": 3972,
      "URL": "https://www.elsevier.com/open-access/userlicense/1.0/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2002,
        9
      ]
    ]
  },
  "DOI": "10.1016/s0304-4149(02)00124-2",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        10,
        14
      ]
    ],
    "date-time": "2002-10-14T21:51:46Z",
    "timestamp": 1034632306000
  },
  "page": "69-82",
  "source": "Crossref",
  "is-referenced-by-count": 80,
  "title": "The threshold regime of finite volume bootstrap percolation",
  "prefix": "10.1016",
  "volume": "101",
  "author": [
    {
      "given": "R.",
      "family": "Cerf",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "F.",
      "family": "Manzo",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB1",
      "doi-asserted-by": "crossref",
      "first-page": "453",
      "DOI": "10.1016/0378-4371(91)90295-N",
      "article-title": "Bootstrap percolation",
      "volume": "171",
      "author": "Adler",
      "year": "1991",
      "journal-title": "Physica A"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB2",
      "doi-asserted-by": "crossref",
      "first-page": "1387",
      "DOI": "10.1088/0305-4470/21/6/015",
      "article-title": "Diffusion percolation: I. Infinite time limit and bootstrap percolation",
      "volume": "21",
      "author": "Adler",
      "year": "1988",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB3",
      "doi-asserted-by": "crossref",
      "first-page": "L297",
      "DOI": "10.1088/0305-4470/22/7/008",
      "article-title": "Comparison of bootstrap percolation models",
      "volume": "22",
      "author": "Adler",
      "year": "1989",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB4",
      "doi-asserted-by": "crossref",
      "first-page": "323",
      "DOI": "10.1007/BF01314923",
      "article-title": "Finite-size effects for some bootstrap percolation models",
      "volume": "60",
      "author": "Adler",
      "year": "1990",
      "journal-title": "J. Statist. Phys."
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB5",
      "doi-asserted-by": "crossref",
      "first-page": "3801",
      "DOI": "10.1088/0305-4470/21/19/017",
      "article-title": "Metastability effects in bootstrap percolation",
      "volume": "21",
      "author": "Aizenman",
      "year": "1988",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB6",
      "doi-asserted-by": "crossref",
      "first-page": "L373",
      "DOI": "10.1088/0022-3719/17/14/001",
      "volume": "17",
      "author": "Branco",
      "year": "1984",
      "journal-title": "J. Phys. C"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB7",
      "doi-asserted-by": "crossref",
      "first-page": "1909",
      "DOI": "10.1088/0022-3719/19/12/006",
      "volume": "19",
      "author": "Branco",
      "year": "1986",
      "journal-title": "J. Phys. C"
    },
    {
      "issue": "4",
      "key": "10.1016/S0304-4149(02)00124-2_BIB8",
      "doi-asserted-by": "crossref",
      "first-page": "1837",
      "DOI": "10.1214/aop/1022874817",
      "article-title": "Finite size scaling in three-dimensional bootstrap percolation",
      "volume": "27",
      "author": "Cerf",
      "year": "1999",
      "journal-title": "Ann. Probab."
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB9",
      "doi-asserted-by": "crossref",
      "first-page": "L31",
      "DOI": "10.1088/0022-3719/12/1/008",
      "article-title": "Bootstrap percolation on a Bethe lattice",
      "volume": "12",
      "author": "Chalupa",
      "year": "1979",
      "journal-title": "J. Phys. C"
    },
    {
      "issue": "1",
      "key": "10.1016/S0304-4149(02)00124-2_BIB10",
      "doi-asserted-by": "crossref",
      "first-page": "123",
      "DOI": "10.1007/s004400050079",
      "article-title": "A nucleation-and-growth model",
      "volume": "107",
      "author": "Dehghanpour",
      "year": "1997",
      "journal-title": "Probab. Theory Related Fields"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB11",
      "doi-asserted-by": "crossref",
      "first-page": "943",
      "DOI": "10.1007/BF01019705",
      "article-title": "Proof of Straley's argument for bootstrap percolation",
      "volume": "48",
      "author": "van Enter",
      "year": "1987",
      "journal-title": "J. Statist. Phys."
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB12",
      "doi-asserted-by": "crossref",
      "first-page": "505",
      "DOI": "10.1007/BF01020891",
      "article-title": "Addendum: finite-size effects for some bootstrap percolation models",
      "volume": "62",
      "author": "van Enter",
      "year": "1991",
      "journal-title": "J. Statist. Phys."
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB13",
      "series-title": "Percolation",
      "author": "Grimmett",
      "year": "1999"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB14",
      "doi-asserted-by": "crossref",
      "first-page": "L233",
      "DOI": "10.1088/0022-3719/18/9/008",
      "volume": "18",
      "author": "Khan",
      "year": "1985",
      "journal-title": "J. Phys. C"
    },
    {
      "issue": "4",
      "key": "10.1016/S0304-4149(02)00124-2_BIB15",
      "first-page": "549",
      "article-title": "Relaxation patterns for competing metastable states: a nucleation and growth model",
      "volume": "4",
      "author": "Manzo",
      "year": "1998",
      "journal-title": "Markov Process. Related Fields"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB16",
      "doi-asserted-by": "crossref",
      "first-page": "185",
      "DOI": "10.1016/0304-4149(94)00061-W",
      "article-title": "Critical length for semi-oriented bootstrap percolation",
      "volume": "56",
      "author": "Mountford",
      "year": "1995",
      "journal-title": "Stochastic Process. Appl."
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB17",
      "doi-asserted-by": "crossref",
      "first-page": "1239",
      "DOI": "10.1007/BF01026574",
      "article-title": "Critical Points of two-dimensional bootstrap percolation-like cellular automata",
      "volume": "58",
      "author": "Schonmann",
      "year": "1990",
      "journal-title": "J. Statist. Phys."
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB18",
      "doi-asserted-by": "crossref",
      "first-page": "619",
      "DOI": "10.1016/0378-4371(90)90280-6",
      "article-title": "Finite size scaling behavior of a biased majority rule cellular automaton",
      "volume": "167",
      "author": "Schonmann",
      "year": "1990",
      "journal-title": "Phys. A"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB19",
      "doi-asserted-by": "crossref",
      "first-page": "174",
      "DOI": "10.1214/aop/1176989923",
      "article-title": "On the behavior of some cellular automata related to bootstrap percolation",
      "volume": "20",
      "author": "Schonmann",
      "year": "1992",
      "journal-title": "Ann. Probab."
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB20",
      "doi-asserted-by": "crossref",
      "first-page": "96",
      "DOI": "10.1016/0167-2789(84)90253-7",
      "article-title": "Simulating physics with cellular automata",
      "volume": "10",
      "author": "Vichniac",
      "year": "1984",
      "journal-title": "Phys. D"
    },
    {
      "key": "10.1016/S0304-4149(02)00124-2_BIB21",
      "doi-asserted-by": "crossref",
      "first-page": "601",
      "DOI": "10.1103/RevModPhys.55.601",
      "article-title": "Statistical mechanics of cellular automata",
      "volume": "55",
      "author": "Wolfram",
      "year": "1983",
      "journal-title": "Rev. Modern Phys."
    }
  ],
  "container-title": "Stochastic Processes and their Applications",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0304414902001242?httpAccept=text/xml",
      "content-type": "text/xml",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0304414902001242?httpAccept=text/plain",
      "content-type": "text/plain",
      "content-version": "vor",
      "intended-application": "text-mining"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        4,
        13
      ]
    ],
    "date-time": "2019-04-13T17:55:22Z",
    "timestamp": 1555178122000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S0304414902001242"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2002,
        9
      ]
    ]
  },
  "references-count": 21,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          2002,
          9
        ]
      ]
    }
  },
  "alternative-id": [
    "S0304414902001242"
  ],
  "URL": "http://dx.doi.org/10.1016/S0304-4149(02)00124-2",
  "relation": {},
  "ISSN": [
    "0304-4149"
  ],
  "subject": [],
  "container-title-short": "Stochastic Processes and their Applications",
  "published": {
    "date-parts": [
      [
        2002,
        9
      ]
    ]
  }
}