{"id":"https://openalex.org/W138938013","doi":null,"title":"A note on a corollary of the shape theorem for the contact process","display_name":"A note on a corollary of the shape theorem for the contact process","publication_year":2013,"publication_date":"2013-11-12","ids":{"openalex":"https://openalex.org/W138938013","mag":"138938013"},"language":"en","primary_location":{"id":"mag:138938013","doi":null,"is_oa":true,"landing_page_url":"https://128.84.21.199/abs/1311.2958v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://128.84.21.199/abs/1311.2958v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035987629","display_name":"Achillefs Tzioufas","orcid":"https://orcid.org/0000-0002-7453-7535","observed_orcids":["https://orcid.org/0000-0002-7453-7535"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Achillefs Tzioufas","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7453-7535","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5035987629"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/contact-process","display_name":"contact process","score":0.9729999899864197},{"id":"https://openalex.org/keywords/shape-theorem","display_name":"shape theorem","score":0.996999979019165},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.49300000071525574},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"integer lattice","score":0.6549999713897705},{"id":"https://openalex.org/keywords/percolation","display_name":"percolation","score":0.5550000071525574}],"concepts":[{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.9897303581237793},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8136492967605591},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7051891684532166},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6790710687637329},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5384364724159241},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.47806623578071594},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.46842730045318604},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38466811180114746},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3828113377094269},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23797038197517395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21534156799316406},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.09575793147087097},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07191470265388489},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:138938013","doi":null,"is_oa":true,"landing_page_url":"https://128.84.21.199/abs/1311.2958v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:138938013","doi":null,"is_oa":true,"landing_page_url":"https://128.84.21.199/abs/1311.2958v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W9763375","https://openalex.org/W60035229","https://openalex.org/W76152643","https://openalex.org/W243736044","https://openalex.org/W596251256","https://openalex.org/W936814640","https://openalex.org/W1491688526","https://openalex.org/W1521233381","https://openalex.org/W1540944551","https://openalex.org/W1584772220","https://openalex.org/W1832313404","https://openalex.org/W1970639502","https://openalex.org/W1992734731","https://openalex.org/W1994817761","https://openalex.org/W2001346830","https://openalex.org/W2017422206","https://openalex.org/W2019654448","https://openalex.org/W2021848502","https://openalex.org/W2038680818","https://openalex.org/W2044617032","https://openalex.org/W2051314659","https://openalex.org/W2051682176","https://openalex.org/W2053928975","https://openalex.org/W2059624491","https://openalex.org/W2089512355","https://openalex.org/W2090008976"],"related_works":["https://openalex.org/W2263154413","https://openalex.org/W7077498943","https://openalex.org/W2170057367","https://openalex.org/W1677890940","https://openalex.org/W2122529828","https://openalex.org/W1992734731","https://openalex.org/W2292482531","https://openalex.org/W2148485152","https://openalex.org/W4310835131","https://openalex.org/W2963813708"],"abstract_inverted_index":{"A":[0],"gentle":[1],"revising":[2],"of":[3,9,63,71,85],"a":[4,75,82],"merely":[5],"using":[6],"basics":[7],"corollary":[8],"the":[10,61,86,94],"shape":[11],"theorem":[12],"pointed":[13],"out":[14,27],"in":[15,23,28,74,90,97],"[8],":[16],"see":[17],"also":[18,56],"[9,":[19],"11],":[20],"for":[21,93],"filling":[22],"some":[24],"lines":[25],"missing":[26],"[7]":[29],"is":[30,80],"shown":[31],"to":[32,51,59],"imply":[33],"that":[34,53],"its":[35],"lower":[36],"bound":[37],"part":[38],"conclusion":[39],"may":[40,55],"take":[41],"effect":[42],"from":[43,66],"time":[44],"zero":[45],"with":[46],"non-zero":[47],"probability,":[48],"and":[49],"leads":[50],"observe":[52],"it":[54],"be":[57],"used":[58],"extend":[60],"formation":[62],"descendancy":[64],"barriers":[65],"[2]":[67],"on":[68],"integer":[69],"lattices":[70],"several":[72],"dimensions":[73],"simple":[76],"way,":[77],"which":[78],"however":[79],"only":[81],"special":[83],"case":[84],"notably":[87],"novel":[88],"results":[89],"[5]":[91],"accomplished":[92],"generalization":[95],"introduced":[96],"[1]":[98],"first.":[99]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}