The Concentration of Measure Phenomenon

Name: Work Video:
Duration: 3 min 30 s
Description: Concentration functions and inequalities Isoperimetric and functional examples Concentration and geometry Concentration in product spaces Entropy and concentration Transportation cost inequalities Sharp bounds of Gaussian and empirical processes Selected applications References Index.
Michel Ledoux
{'id': 'https://openalex.org/W1573820523', 'doi': 'https://doi.org/10.1090/surv/089', 'title': 'The Concentration of Measure Phenomenon', 'display_name': 'The Concentration of Measure Phenomenon', 'publication_year': 2005, 'publication_date': '2005-02-14', 'ids': {'openalex': 'https://openalex.org/W1573820523', 'doi': 'https://doi.org/10.1090/surv/089', 'mag': '1573820523'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/surv/089', 'pdf_url': 'http://www.ams.org/surv/089/surv089.pdf', 'source': {'id': 'https://openalex.org/S4210235382', 'display_name': 'Mathematical surveys', 'issn_l': '0076-5376', 'issn': ['0076-5376'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'book series'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'book', 'type_crossref': 'monograph', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'http://www.ams.org/surv/089/surv089.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5005191959', 'display_name': 'Michel Ledoux', 'orcid': 'https://orcid.org/0000-0002-4438-5366'}, 'institutions': [{'id': 'https://openalex.org/I134560555', 'display_name': 'Université Toulouse III - Paul Sabatier', 'ror': 'https://ror.org/02v6kpv12', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I134560555']}], 'countries': ['FR'], 'is_corresponding': True, 'raw_author_name': 'Michel Ledoux', 'raw_affiliation_strings': ['Université Paul Sabatier, Toulouse, France'], 'affiliations': [{'raw_affiliation_string': 'Université Paul Sabatier, Toulouse, France', 'institution_ids': ['https://openalex.org/I134560555']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5005191959'], 'corresponding_institution_ids': ['https://openalex.org/I134560555'], 'apc_list': None, 'apc_paid': None, 'fwci': 19.053, 'has_fulltext': False, 'cited_by_count': 1992, 'citation_normalized_percentile': {'value': 0.986667, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 99, 'max': 100}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12516', 'display_name': 'Advanced Mathematical Theories and Applications', 'score': 0.7387, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T12516', 'display_name': 'Advanced Mathematical Theories and Applications', 'score': 0.7387, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear 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/T10963', 'display_name': 'Advanced Optimization Algorithms Research', 'score': 0.6459, 'subfield': {'id': 'https://openalex.org/subfields/2612', 'display_name': 'Numerical Analysis'}, '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/T11106', 'display_name': 'Data Management and Algorithms', 'score': 0.6142, 'subfield': {'id': 'https://openalex.org/subfields/1711', 'display_name': 'Signal Processing'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/concentration-of-measure', 'display_name': 'Concentration of measure', 'score': 0.4479305}], 'concepts': [{'id': 'https://openalex.org/C140142295', 'wikidata': 'https://www.wikidata.org/wiki/Q617417', 'display_name': 'Isoperimetric inequality', 'level': 2, 'score': 0.8971995}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.5554272}, {'id': 'https://openalex.org/C2780009758', 'wikidata': 'https://www.wikidata.org/wiki/Q6804172', 'display_name': 'Measure (data warehouse)', 'level': 2, 'score': 0.52363896}, {'id': 'https://openalex.org/C106301342', 'wikidata': 'https://www.wikidata.org/wiki/Q4117933', 'display_name': 'Entropy (arrow of time)', 'level': 2, 'score': 0.521202}, {'id': 'https://openalex.org/C163716315', 'wikidata': 'https://www.wikidata.org/wiki/Q901177', 'display_name': 'Gaussian', 'level': 2, 'score': 0.46279028}, {'id': 'https://openalex.org/C84498859', 'wikidata': 'https://www.wikidata.org/wiki/Q5158327', 'display_name': 'Concentration of measure', 'level': 2, 'score': 0.4479305}, {'id': 'https://openalex.org/C2777382242', 'wikidata': 'https://www.wikidata.org/wiki/Q6017816', 'display_name': 'Index (typography)', 'level': 2, 'score': 0.44568363}, {'id': 'https://openalex.org/C121864883', 'wikidata': 'https://www.wikidata.org/wiki/Q677916', 'display_name': 'Statistical physics', 'level': 1, 'score': 0.3672397}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.29648316}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.2944923}, {'id': 'https://openalex.org/C97355855', 'wikidata': 'https://www.wikidata.org/wiki/Q11473', 'display_name': 'Thermodynamics', 'level': 1, 'score': 0.2920094}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.24797839}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.24132892}, {'id': 'https://openalex.org/C124101348', 'wikidata': 'https://www.wikidata.org/wiki/Q172491', 'display_name': 'Data mining', 'level': 1, 'score': 0.12194824}, {'id': 'https://openalex.org/C147597530', 'wikidata': 'https://www.wikidata.org/wiki/Q369472', 'display_name': 'Computational chemistry', 'level': 1, 'score': 0.105814815}, {'id': 'https://openalex.org/C136764020', 'wikidata': 'https://www.wikidata.org/wiki/Q466', 'display_name': 'World Wide Web', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/surv/089', 'pdf_url': 'http://www.ams.org/surv/089/surv089.pdf', 'source': {'id': 'https://openalex.org/S4210235382', 'display_name': 'Mathematical surveys', 'issn_l': '0076-5376', 'issn': ['0076-5376'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'book series'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://www.gbv.de/dms/bowker/toc/9780821837924.pdf', 'pdf_url': 'http://www.gbv.de/dms/bowker/toc/9780821837924.pdf', 'source': {'id': 'https://openalex.org/S4308707206', 'display_name': 'Library Union Catalog of Bavaria, Berlin and Brandenburg (B3Kat Repository)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I157725225', 'host_organization_name': 'University of Illinois Urbana-Champaign', 'host_organization_lineage': ['https://openalex.org/I157725225'], 'host_organization_lineage_names': ['University of Illinois Urbana-Champaign'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/surv/089', 'pdf_url': 'http://www.ams.org/surv/089/surv089.pdf', 'source': {'id': 'https://openalex.org/S4210235382', 'display_name': 'Mathematical surveys', 'issn_l': '0076-5376', 'issn': ['0076-5376'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'book series'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [{'score': 0.55, 'display_name': 'Decent work and economic growth', 'id': 'https://metadata.un.org/sdg/8'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4387415199', 'https://openalex.org/W4299574858', 'https://openalex.org/W4297475888', 'https://openalex.org/W4293733602', 'https://openalex.org/W2952030842', 'https://openalex.org/W2799900090', 'https://openalex.org/W2587882711', 'https://openalex.org/W2393012656', 'https://openalex.org/W2047527454', 'https://openalex.org/W2042006853'], 'abstract_inverted_index': {'Concentration': [0, 8, 11], 'functions': [1], 'and': [2, 5, 9, 16, 25], 'inequalities': [3, 20], 'Isoperimetric': [4], 'functional': [6], 'examples': [7], 'geometry': [10], 'in': [12], 'product': [13], 'spaces': [14], 'Entropy': [15], 'concentration': [17], 'Transportation': [18], 'cost': [19], 'Sharp': [21], 'bounds': [22], 'of': [23], 'Gaussian': [24], 'empirical': [26], 'processes': [27], 'Selected': [28], 'applications': [29], 'References': [30], 'Index.': [31]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1573820523', 'counts_by_year': [{'year': 2024, 'cited_by_count': 33}, {'year': 2023, 'cited_by_count': 47}, {'year': 2022, 'cited_by_count': 63}, {'year': 2021, 'cited_by_count': 138}, {'year': 2020, 'cited_by_count': 104}, {'year': 2019, 'cited_by_count': 129}, {'year': 2018, 'cited_by_count': 98}, {'year': 2017, 'cited_by_count': 119}, {'year': 2016, 'cited_by_count': 85}, {'year': 2015, 'cited_by_count': 131}, {'year': 2014, 'cited_by_count': 122}, {'year': 2013, 'cited_by_count': 142}, {'year': 2012, 'cited_by_count': 112}], 'updated_date': '2024-12-22T19:38:07.925613', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
