{"id":"https://openalex.org/W2963340341","doi":"https://doi.org/10.1137/120887382","title":"Computing Bounds for Entropy of Stationary $\\mathbb{Z}^d$ Markov Random Fields","display_name":"Computing Bounds for Entropy of Stationary $\\mathbb{Z}^d$ Markov Random Fields","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2963340341","doi":"https://doi.org/10.1137/120887382","mag":"2963340341"},"language":"en","primary_location":{"id":"doi:10.1137/120887382","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120887382","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113544364","display_name":"Brian Marcus","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Brian Marcus","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023789848","display_name":"Ronnie Pavlov","orcid":"https://orcid.org/0000-0003-3363-9284"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronnie Pavlov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113544364"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6066,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86067864,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"3","first_page":"1544","last_page":"1558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9932000041007996,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9922000169754028,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7925229072570801},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6705948114395142},{"id":"https://openalex.org/keywords/gibbs-measure","display_name":"Gibbs measure","score":0.5857048034667969},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5629671216011047},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5580753087997437},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4830913543701172},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.47117406129837036},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.40933746099472046},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2289341688156128},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.163493812084198},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08021971583366394},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0703417956829071}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7925229072570801},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6705948114395142},{"id":"https://openalex.org/C158444337","wikidata":"https://www.wikidata.org/wiki/Q2510435","display_name":"Gibbs measure","level":2,"score":0.5857048034667969},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5629671216011047},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5580753087997437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4830913543701172},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.47117406129837036},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40933746099472046},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2289341688156128},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.163493812084198},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08021971583366394},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0703417956829071},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120887382","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120887382","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1494720687","https://openalex.org/W1565611252","https://openalex.org/W1975433306","https://openalex.org/W1985908422","https://openalex.org/W1998959913","https://openalex.org/W2004724832","https://openalex.org/W2029668118","https://openalex.org/W2031521232","https://openalex.org/W2036877243","https://openalex.org/W2079675572","https://openalex.org/W2113770815","https://openalex.org/W2132353975","https://openalex.org/W2952865985","https://openalex.org/W2953053085","https://openalex.org/W2963814981","https://openalex.org/W3104955770"],"related_works":["https://openalex.org/W1660242800","https://openalex.org/W2077211377","https://openalex.org/W1006270037","https://openalex.org/W3152686072","https://openalex.org/W3129238073","https://openalex.org/W2056274461","https://openalex.org/W162527578","https://openalex.org/W2517044585","https://openalex.org/W35519032","https://openalex.org/W2354828774"],"abstract_inverted_index":{"For":[0],"any":[1],"stationary":[2],"$\\mathbb{Z}^d$":[3],"Gibbs":[4],"measure":[5],"that":[6,19,35],"satisfies":[7],"strong":[8],"spatial":[9],"mixing,":[10],"we":[11],"obtain":[12],"sequences":[13],"of":[14],"upper":[15],"and":[16,42],"lower":[17],"approximations":[18,29],"converge":[20],"to":[21,39],"its":[22],"entropy.":[23],"In":[24],"the":[25,33],"case":[26],"$d=2$,":[27],"these":[28],"are":[30,37],"efficient":[31],"in":[32,46,49],"sense":[34],"they":[36],"accurate":[38],"within":[40],"$\\epsilon$":[41],"can":[43],"be":[44],"computed":[45],"time":[47],"polynomial":[48],"$1/\\epsilon$.":[50]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
