The law of large numbers for the bigraded Betti numbers of a random simplicial complex

Name: Work Video:
Duration: 3 min 30 s
Description: This note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of a larger work in progress is included in the concluding remarks.
Djordje Baralić; Vlada Limic
{'id': 'https://openalex.org/W2998961566', 'doi': 'https://doi.org/10.1070/rm9936', 'title': 'The law of large numbers for the bigraded Betti numbers of a random simplicial complex', 'display_name': 'The law of large numbers for the bigraded Betti numbers of a random simplicial complex', 'publication_year': 2021, 'publication_date': '2021-02-01', 'ids': {'openalex': 'https://openalex.org/W2998961566', 'doi': 'https://doi.org/10.1070/rm9936', 'mag': '2998961566'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1070/rm9936', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S132681663', 'display_name': 'Russian Mathematical Surveys', 'issn_l': '0036-0279', 'issn': ['0036-0279', '1468-4829', '1473-2009'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320083', 'host_organization_name': 'IOP Publishing', 'host_organization_lineage': ['https://openalex.org/P4310311669', 'https://openalex.org/P4310320083'], 'host_organization_lineage_names': ['Institute of Physics', 'IOP Publishing'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'http://arxiv.org/pdf/2001.02105', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5073589051', 'display_name': 'Djordje Baralić', 'orcid': 'https://orcid.org/0000-0003-2836-7958'}, 'institutions': [{'id': 'https://openalex.org/I1294671590', 'display_name': 'Centre National de la Recherche Scientifique', 'ror': 'https://ror.org/02feahw73', 'country_code': 'FR', 'type': 'government', 'lineage': ['https://openalex.org/I1294671590']}, {'id': 'https://openalex.org/I68947357', 'display_name': 'Université de Strasbourg', 'ror': 'https://ror.org/00pg6eq24', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I68947357']}], 'countries': ['FR'], 'is_corresponding': True, 'raw_author_name': 'D. Baralić', 'raw_affiliation_strings': ["IRMA, UMR 7501 de l'Université de Strasbourg et du CNRS, 7 Rue René Descartes, 67084, Strasbourg Cedex, France"], 'affiliations': [{'raw_affiliation_string': "IRMA, UMR 7501 de l'Université de Strasbourg et du CNRS, 7 Rue René Descartes, 67084, Strasbourg Cedex, France", 'institution_ids': ['https://openalex.org/I1294671590', 'https://openalex.org/I68947357']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5028599054', 'display_name': 'Vlada Limic', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I68947357', 'display_name': 'Université de Strasbourg', 'ror': 'https://ror.org/00pg6eq24', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I68947357']}, {'id': 'https://openalex.org/I1294671590', 'display_name': 'Centre National de la Recherche Scientifique', 'ror': 'https://ror.org/02feahw73', 'country_code': 'FR', 'type': 'government', 'lineage': ['https://openalex.org/I1294671590']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'V. Limic', 'raw_affiliation_strings': ["IRMA, UMR 7501 de l'Université de Strasbourg et du CNRS, 7 Rue René Descartes, 67084, Strasbourg Cedex, France"], 'affiliations': [{'raw_affiliation_string': "IRMA, UMR 7501 de l'Université de Strasbourg et du CNRS, 7 Rue René Descartes, 67084, Strasbourg Cedex, France", 'institution_ids': ['https://openalex.org/I68947357', 'https://openalex.org/I1294671590']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': ['https://openalex.org/A5073589051'], 'corresponding_institution_ids': ['https://openalex.org/I1294671590', 'https://openalex.org/I68947357'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 57}, 'biblio': {'volume': '76', 'issue': '1', 'first_page': '186', 'last_page': '189'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12536', 'display_name': 'Topological and Geometric Data Analysis', 'score': 0.9997, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T12536', 'display_name': 'Topological and Geometric Data Analysis', 'score': 0.9997, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10948', 'display_name': 'Advanced Combinatorial Mathematics', 'score': 0.9992, 'subfield': {'id': 'https://openalex.org/subfields/2607', 'display_name': 'Discrete Mathematics and Combinatorics'}, '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/T10588', 'display_name': 'Mathematical Dynamics and Fractals', 'score': 0.994, '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/algebraic-topology', 'display_name': 'Algebraic topology', 'score': 0.7619809}, {'id': 'https://openalex.org/keywords/frontier', 'display_name': 'Frontier', 'score': 0.5985927}], 'concepts': [{'id': 'https://openalex.org/C129621563', 'wikidata': 'https://www.wikidata.org/wiki/Q429593', 'display_name': 'Betti number', 'level': 2, 'score': 0.8989688}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8157908}, {'id': 'https://openalex.org/C145054310', 'wikidata': 'https://www.wikidata.org/wiki/Q212803', 'display_name': 'Algebraic topology', 'level': 3, 'score': 0.7619809}, {'id': 'https://openalex.org/C9376300', 'wikidata': 'https://www.wikidata.org/wiki/Q168817', 'display_name': 'Algebraic number', 'level': 2, 'score': 0.5999023}, {'id': 'https://openalex.org/C2778571376', 'wikidata': 'https://www.wikidata.org/wiki/Q1355821', 'display_name': 'Frontier', 'level': 2, 'score': 0.5985927}, {'id': 'https://openalex.org/C185767445', 'wikidata': 'https://www.wikidata.org/wiki/Q207952', 'display_name': 'Law of large numbers', 'level': 3, 'score': 0.54562527}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.32716238}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.32173568}, {'id': 'https://openalex.org/C199539241', 'wikidata': 'https://www.wikidata.org/wiki/Q7748', 'display_name': 'Law', 'level': 1, 'score': 0.18792662}, {'id': 'https://openalex.org/C122123141', 'wikidata': 'https://www.wikidata.org/wiki/Q176623', 'display_name': 'Random variable', 'level': 2, 'score': 0.16717699}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.0933772}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.08909151}, {'id': 'https://openalex.org/C17744445', 'wikidata': 'https://www.wikidata.org/wiki/Q36442', 'display_name': 'Political science', 'level': 0, 'score': 0.05095756}, {'id': 'https://openalex.org/C5961521', 'wikidata': 'https://www.wikidata.org/wiki/Q746083', 'display_name': 'Homotopy', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1070/rm9936', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S132681663', 'display_name': 'Russian Mathematical Surveys', 'issn_l': '0036-0279', 'issn': ['0036-0279', '1468-4829', '1473-2009'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320083', 'host_organization_name': 'IOP Publishing', 'host_organization_lineage': ['https://openalex.org/P4310311669', 'https://openalex.org/P4310320083'], 'host_organization_lineage_names': ['Institute of Physics', 'IOP Publishing'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/2001.02105', 'pdf_url': 'http://arxiv.org/pdf/2001.02105', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2001.02105', 'pdf_url': 'https://arxiv.org/pdf/2001.02105', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/2001.02105', 'pdf_url': 'http://arxiv.org/pdf/2001.02105', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [{'id': 'https://metadata.un.org/sdg/16', 'display_name': 'Peace, justice, and strong institutions', 'score': 0.43}], 'grants': [{'funder': 'https://openalex.org/F4320322364', 'funder_display_name': 'Labex', 'award_id': None}], 'datasets': [], 'versions': [], 'referenced_works_count': 6, 'referenced_works': ['https://openalex.org/W1982599181', 'https://openalex.org/W2018582120', 'https://openalex.org/W2157071288', 'https://openalex.org/W2315238595', 'https://openalex.org/W3083418760', 'https://openalex.org/W9575071'], 'related_works': ['https://openalex.org/W3175677173', 'https://openalex.org/W3134800435', 'https://openalex.org/W2998961566', 'https://openalex.org/W25586180', 'https://openalex.org/W2347401120', 'https://openalex.org/W2334292868', 'https://openalex.org/W2310010941', 'https://openalex.org/W2095493290', 'https://openalex.org/W1988132375', 'https://openalex.org/W1517300152'], 'abstract_inverted_index': {'This': [0], 'note': [1], 'announces': [2], 'recent': [3], 'exciting': [4], 'progress': [5, 38], 'on': [6], 'the': [7, 42], 'frontier': [8], 'between': [9], 'algebraic': [10], 'topology': [11], 'and': [12], 'probability': [13], 'theory.': [14], 'It': [15], 'is': [16, 39], 'intended': [17], 'for': [18], 'a': [19, 34], 'journal': [20], 'which': [21], 'publishes': [22], 'such': [23], 'announcements': [24], '(without': [25], 'an': [26], 'abstract,': [27], 'typically': [28], 'in': [29, 37, 41], 'Russian).': [30], 'A': [31], 'description': [32], 'of': [33], 'larger': [35], 'work': [36], 'included': [40], 'concluding': [43], 'remarks.': [44]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2998961566', 'counts_by_year': [], 'updated_date': '2024-12-08T01:02:06.920814', 'created_date': '2020-01-23'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
