{"id":"https://openalex.org/W3094827148","doi":"https://doi.org/10.3390/e23010069","title":"On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement","display_name":"On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement","publication_year":2021,"publication_date":"2021-01-04","ids":{"openalex":"https://openalex.org/W3094827148","doi":"https://doi.org/10.3390/e23010069","mag":"3094827148","pmid":"https://pubmed.ncbi.nlm.nih.gov/33406669"},"language":"en","primary_location":{"id":"doi:10.3390/e23010069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010069","pdf_url":"https://www.mdpi.com/1099-4300/23/1/69/pdf?version=1609820792","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/1/69/pdf?version=1609820792","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zhenhao Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenhao Cai","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing 100871, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing 100871, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yunfeng Xiong","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunfeng Xiong","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing 100871, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing 100871, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yuan Zhang","orcid":"https://orcid.org/0000-0002-8408-5755"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing 100871, China"],"raw_orcid":"https://orcid.org/0000-0002-8408-5755","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing 100871, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.1477,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84681144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"1","first_page":"69","last_page":"69"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.477400004863739,"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":0.477400004863739,"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":0.21770000457763672,"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/T11716","display_name":"Random Matrices and Applications","score":0.03759999945759773,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/finitary","display_name":"Finitary","score":0.9656000137329102},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6067000031471252},{"id":"https://openalex.org/keywords/fiber","display_name":"Fiber","score":0.5389000177383423},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5358999967575073},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4546999931335449},{"id":"https://openalex.org/keywords/phase-diagram","display_name":"Phase diagram","score":0.439300000667572}],"concepts":[{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.9656000137329102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6958000063896179},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6067000031471252},{"id":"https://openalex.org/C519885992","wikidata":"https://www.wikidata.org/wiki/Q161","display_name":"Fiber","level":2,"score":0.5389000177383423},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5358999967575073},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.439300000667572},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33570000529289246},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3296000063419342},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2930000126361847},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.29170000553131104},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26330000162124634},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.26170000433921814}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e23010069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010069","pdf_url":"https://www.mdpi.com/1099-4300/23/1/69/pdf?version=1609820792","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33406669","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33406669","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:arXiv.org:2010.14254","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.14254","pdf_url":"https://arxiv.org/pdf/2010.14254","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,"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":null,"raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7824420","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7824420","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:532654911d1d44b6924be10262a004af","is_oa":true,"landing_page_url":"https://doaj.org/article/532654911d1d44b6924be10262a004af","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 1, p 69 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/1/69/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23010069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 23; Issue 1; Pages: 69","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23010069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010069","pdf_url":"https://www.mdpi.com/1099-4300/23/1/69/pdf?version=1609820792","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6481552161","display_name":null,"funder_award_id":"Nos. 2020TQ0011","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3094827148.pdf","grobid_xml":"https://content.openalex.org/works/W3094827148.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W589246141","https://openalex.org/W1926512643","https://openalex.org/W1944151680","https://openalex.org/W2034367515","https://openalex.org/W2034477758","https://openalex.org/W2034715235","https://openalex.org/W2041438517","https://openalex.org/W2071916136","https://openalex.org/W2962714469","https://openalex.org/W2963795525","https://openalex.org/W3170187968","https://openalex.org/W6678261740","https://openalex.org/W6825680077"],"related_works":[],"abstract_inverted_index":{"In":[0,22],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,16,25,50,58],"evolution":[6],"of":[7,19,62],"a":[8,63],"Finitary":[9],"Random":[10],"Interlacement":[11],"(FRI)":[12],"with":[13,79],"respect":[14,80],"to":[15,24,73,81],"expected":[17],"length":[18,47],"each":[20],"fiber.":[21],"contrast":[23],"previously":[26],"proved":[27],"phase":[28],"transition":[29],"between":[30],"sufficiently":[31],"large":[32],"and":[33,60,71],"small":[34],"fiber":[35,46,65],"length,":[36,66],"for":[37],"all":[38],"d\u22653,":[39],"FRI":[40],"is":[41,68],"NOT":[42],"stochastically":[43],"monotone":[44],"as":[45],"increases.":[48],"At":[49],"same":[51],"time,":[52],"numerical":[53],"evidence":[54],"still":[55],"strongly":[56],"supports":[57],"existence":[59],"uniqueness":[61],"critical":[64],"which":[67],"estimated":[69],"theoretically":[70],"numerically":[72],"be":[74],"an":[75],"inversely":[76],"proportional":[77],"function":[78],"system":[82],"intensity.":[83]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2020-11-09T00:00:00"}