Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W1981225903', 'doi': 'https://doi.org/10.1214/aop/1048516527', 'title': 'Euler characteristics for Gaussian fields on manifolds', 'display_name': 'Euler characteristics for Gaussian fields on manifolds', 'publication_year': 2003, 'publication_date': '2003-03-24', 'ids': {'openalex': 'https://openalex.org/W1981225903', 'doi': 'https://doi.org/10.1214/aop/1048516527', 'mag': '1981225903'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1214/aop/1048516527', 'pdf_url': 'https://projecteuclid.org/journals/annals-of-probability/volume-31/issue-2/Euler-characteristics-for-Gaussian-fields-on-manifolds/10.1214/aop/1048516527.pdf', 'source': {'id': 'https://openalex.org/S40212770', 'display_name': 'The Annals of Probability', 'issn_l': '0091-1798', 'issn': ['0091-1798', '2168-894X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319881', 'host_organization_name': 'Institute of Mathematical Statistics', 'host_organization_lineage': ['https://openalex.org/P4310319881'], 'host_organization_lineage_names': ['Institute of Mathematical Statistics'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://projecteuclid.org/journals/annals-of-probability/volume-31/issue-2/Euler-characteristics-for-Gaussian-fields-on-manifolds/10.1214/aop/1048516527.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5101541844', 'display_name': 'Jonathan Taylor', 'orcid': 'https://orcid.org/0000-0002-6951-999X'}, 'institutions': [{'id': 'https://openalex.org/I97018004', 'display_name': 'Stanford University', 'ror': 'https://ror.org/00f54p054', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I97018004']}, {'id': 'https://openalex.org/I174306211', 'display_name': 'Technion – Israel Institute of Technology', 'ror': 'https://ror.org/03qryx823', 'country_code': 'IL', 'type': 'education', 'lineage': ['https://openalex.org/I174306211']}], 'countries': ['IL', 'US'], 'is_corresponding': False, 'raw_author_name': 'Jonathan E. Taylor', 'raw_affiliation_strings': ['DEPARTMENT OF STATISTICS SEQUOIA HALL STANFORD, CALIFORNIA 94305', 'FACULTY OF INDUSTRIAL ENGINEERING AND MANAGEMENT TECHNION HAIFA 32000 ISRAEL', 'Stanford University and Technion'], 'affiliations': [{'raw_affiliation_string': 'Stanford University and Technion', 'institution_ids': ['https://openalex.org/I97018004']}, {'raw_affiliation_string': 'DEPARTMENT OF STATISTICS SEQUOIA HALL STANFORD, CALIFORNIA 94305', 'institution_ids': []}, {'raw_affiliation_string': 'FACULTY OF INDUSTRIAL ENGINEERING AND MANAGEMENT TECHNION HAIFA 32000 ISRAEL', 'institution_ids': ['https://openalex.org/I174306211']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5029952351', 'display_name': 'Robert J. Adler', 'orcid': 'https://orcid.org/0000-0002-8170-0396'}, 'institutions': [{'id': 'https://openalex.org/I97018004', 'display_name': 'Stanford University', 'ror': 'https://ror.org/00f54p054', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I97018004']}, {'id': 'https://openalex.org/I174306211', 'display_name': 'Technion – Israel Institute of Technology', 'ror': 'https://ror.org/03qryx823', 'country_code': 'IL', 'type': 'education', 'lineage': ['https://openalex.org/I174306211']}], 'countries': ['IL', 'US'], 'is_corresponding': False, 'raw_author_name': 'Robert J. Adler', 'raw_affiliation_strings': ['DEPARTMENT OF STATISTICS SEQUOIA HALL STANFORD, CALIFORNIA 94305', 'FACULTY OF INDUSTRIAL ENGINEERING AND MANAGEMENT TECHNION HAIFA 32000 ISRAEL', 'Stanford University and Technion'], 'affiliations': [{'raw_affiliation_string': 'Stanford University and Technion', 'institution_ids': ['https://openalex.org/I97018004']}, {'raw_affiliation_string': 'DEPARTMENT OF STATISTICS SEQUOIA HALL STANFORD, CALIFORNIA 94305', 'institution_ids': []}, {'raw_affiliation_string': 'FACULTY OF INDUSTRIAL ENGINEERING AND MANAGEMENT TECHNION HAIFA 32000 ISRAEL', 'institution_ids': ['https://openalex.org/I174306211']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 6.414, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 112, 'citation_normalized_percentile': {'value': 0.980772, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 96, 'max': 97}, 'biblio': {'volume': '31', 'issue': '2', 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12351', 'display_name': 'Geometry and complex manifolds', 'score': 0.9981, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, '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/T12351', 'display_name': 'Geometry and complex manifolds', 'score': 0.9981, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, '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/T10229', 'display_name': 'Geometric Analysis and Curvature Flows', 'score': 0.9847, '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'}}, {'id': 'https://openalex.org/T11830', 'display_name': 'Point processes and geometric inequalities', 'score': 0.9608, '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/excursion', 'display_name': 'Excursion', 'score': 0.8446467}, {'id': 'https://openalex.org/keywords/euler-characteristic', 'display_name': 'Euler characteristic', 'score': 0.791971}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8737724}, {'id': 'https://openalex.org/C2780550144', 'wikidata': 'https://www.wikidata.org/wiki/Q1156976', 'display_name': 'Excursion', 'level': 2, 'score': 0.8446467}, {'id': 'https://openalex.org/C196433757', 'wikidata': 'https://www.wikidata.org/wiki/Q852973', 'display_name': 'Euler characteristic', 'level': 2, 'score': 0.791971}, {'id': 'https://openalex.org/C130402806', 'wikidata': 'https://www.wikidata.org/wiki/Q5361768', 'display_name': 'Random field', 'level': 2, 'score': 0.6828365}, {'id': 'https://openalex.org/C163716315', 'wikidata': 'https://www.wikidata.org/wiki/Q901177', 'display_name': 'Gaussian', 'level': 2, 'score': 0.5414112}, {'id': 'https://openalex.org/C62884695', 'wikidata': 'https://www.wikidata.org/wiki/Q184871', 'display_name': "Euler's formula", 'level': 2, 'score': 0.51933706}, {'id': 'https://openalex.org/C178650346', 'wikidata': 'https://www.wikidata.org/wiki/Q201984', 'display_name': 'Covariance', 'level': 2, 'score': 0.48473427}, {'id': 'https://openalex.org/C192939610', 'wikidata': 'https://www.wikidata.org/wiki/Q188444', 'display_name': 'Differential geometry', 'level': 2, 'score': 0.421786}, {'id': 'https://openalex.org/C51267290', 'wikidata': 'https://www.wikidata.org/wiki/Q5527848', 'display_name': 'Gaussian random field', 'level': 4, 'score': 0.41896132}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.40750933}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.39434218}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.35840374}, {'id': 'https://openalex.org/C61326573', 'wikidata': 'https://www.wikidata.org/wiki/Q1496376', 'display_name': 'Gaussian process', 'level': 3, 'score': 0.35653988}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.3433998}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.088269055}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C17744445', 'wikidata': 'https://www.wikidata.org/wiki/Q36442', 'display_name': 'Political science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199539241', 'wikidata': 'https://www.wikidata.org/wiki/Q7748', 'display_name': 'Law', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1214/aop/1048516527', 'pdf_url': 'https://projecteuclid.org/journals/annals-of-probability/volume-31/issue-2/Euler-characteristics-for-Gaussian-fields-on-manifolds/10.1214/aop/1048516527.pdf', 'source': {'id': 'https://openalex.org/S40212770', 'display_name': 'The Annals of Probability', 'issn_l': '0091-1798', 'issn': ['0091-1798', '2168-894X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319881', 'host_organization_name': 'Institute of Mathematical Statistics', 'host_organization_lineage': ['https://openalex.org/P4310319881'], 'host_organization_lineage_names': ['Institute of Mathematical Statistics'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://escholarship.mcgill.ca/concern/theses/zs25xc036', 'pdf_url': 'http://escholarship.mcgill.ca/downloads/c247dv713', 'source': {'id': 'https://openalex.org/S4306401568', 'display_name': 'eScholarship@McGill (McGill)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I5023651', 'host_organization_name': 'McGill University', 'host_organization_lineage': ['https://openalex.org/I5023651'], 'host_organization_lineage_names': ['McGill University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1214/aop/1048516527', 'pdf_url': 'https://projecteuclid.org/journals/annals-of-probability/volume-31/issue-2/Euler-characteristics-for-Gaussian-fields-on-manifolds/10.1214/aop/1048516527.pdf', 'source': {'id': 'https://openalex.org/S40212770', 'display_name': 'The Annals of Probability', 'issn_l': '0091-1798', 'issn': ['0091-1798', '2168-894X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319881', 'host_organization_name': 'Institute of Mathematical Statistics', 'host_organization_lineage': ['https://openalex.org/P4310319881'], 'host_organization_lineage_names': ['Institute of Mathematical Statistics'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 21, 'referenced_works': ['https://openalex.org/W1481438721', 'https://openalex.org/W1562147356', 'https://openalex.org/W1599070578', 'https://openalex.org/W1653384328', 'https://openalex.org/W1979472779', 'https://openalex.org/W1980430435', 'https://openalex.org/W1996931690', 'https://openalex.org/W2009012166', 'https://openalex.org/W2015369872', 'https://openalex.org/W2026892575', 'https://openalex.org/W2034944977', 'https://openalex.org/W2044970534', 'https://openalex.org/W2095487469', 'https://openalex.org/W2137543775', 'https://openalex.org/W2314948770', 'https://openalex.org/W2325410206', 'https://openalex.org/W2772653002', 'https://openalex.org/W2983836991', 'https://openalex.org/W3129186208', 'https://openalex.org/W4205377395', 'https://openalex.org/W4238054270'], 'related_works': ['https://openalex.org/W4285599464', 'https://openalex.org/W4252156009', 'https://openalex.org/W4244438193', 'https://openalex.org/W3101730079', 'https://openalex.org/W3083204305', 'https://openalex.org/W2262012800', 'https://openalex.org/W2090206927', 'https://openalex.org/W2013997342', 'https://openalex.org/W2009012166', 'https://openalex.org/W1987668712'], 'abstract_inverted_index': {'We': [0], 'are': [1, 18, 27], 'interested': [2], 'in': [3, 31], 'the': [4, 23, 48, 66, 72, 86, 95, 98], 'geometric': [5, 43], 'properties': [6, 78], 'of': [7, 19, 54, 58, 65, 79, 89, 102], 'real-valued': [8], 'Gaussian': [9, 61], 'random': [10, 24, 62, 125], 'fields': [11, 25, 33, 126], 'defined': [12], 'on': [13, 35, 122, 127], 'manifolds.': [14], 'Our': [15, 29, 119], 'manifolds,': [16], '$M$,': [17], 'class': [20], '$C^3$': [21], 'and': [22, 41, 110, 133], '$f$': [26], 'smooth.': [28], 'interest': [30, 93], 'these': [32], 'focuses': [34], 'their': [36, 42], 'excursion': [37, 56, 104], 'sets,': [38], '$f^{-1}[u,': [39], '+\\infty)$,': [40], 'properties.': [44], 'Specifically,': [45], 'we': [46], 'derive': [47], 'expected': [49, 99], 'Euler': [50, 100], 'characteristic': [51, 101], '$\\Ee[\\chi(f^{-1}[u,': [52], '+\\infty))]$': [53], 'an': [55, 103], 'set': [57, 105], 'a': [59, 82, 107], 'smooth': [60], 'field.': [63], 'Part': [64], 'motivation': [67], 'for': [68], 'this': [69], 'comes': [70], 'from': [71, 124], 'fact': [73], 'that': [74], '$\\Ee[\\chi(f^{-1}[u,+\\infty))]$': [75], 'relates': [76], 'global': [77], '$M$': [80], 'to': [81, 85], 'geometry': [83], 'related': [84], 'covariance': [87], 'structure': [88], '$f$.': [90], 'Of': [91], 'further': [92], 'is': [94], 'relation': [96], 'between': [97], 'above': [106], 'level': [108], '$u$': [109], '$\\Pp[': [111], '\\sup_{p': [112], '\\in': [113], 'M}': [114], 'f(p)': [115], '\\geq': [116], 'u': [117], ']$.': [118], 'proofs': [120], 'rely': [121], 'results': [123], '$\\Rr^n$': [128], 'as': [129, 131], 'well': [130], 'differential': [132], 'Riemannian': [134], 'geometry.': [135]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1981225903', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2022, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 4}, {'year': 2020, 'cited_by_count': 2}, {'year': 2019, 'cited_by_count': 6}, {'year': 2018, 'cited_by_count': 6}, {'year': 2017, 'cited_by_count': 6}, {'year': 2016, 'cited_by_count': 11}, {'year': 2015, 'cited_by_count': 6}, {'year': 2014, 'cited_by_count': 5}, {'year': 2013, 'cited_by_count': 7}, {'year': 2012, 'cited_by_count': 5}], 'updated_date': '2024-12-15T17:27:56.177616', 'created_date': '2016-06-24'}