{"id":"https://openalex.org/W1999577479","doi":"https://doi.org/10.1137/120895408","title":"Crime Modeling with L\u00e9vy Flights","display_name":"Crime Modeling with L\u00e9vy Flights","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1999577479","doi":"https://doi.org/10.1137/120895408","mag":"1999577479"},"language":"en","primary_location":{"id":"doi:10.1137/120895408","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120895408","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied 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/A5000096589","display_name":"Sorathan Chaturapruek","orcid":null},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sorathan Chaturapruek","raw_affiliation_strings":["Department of Mathematics, Harvey Mudd College, Claremont, CA 91711"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harvey Mudd College, Claremont, CA 91711","institution_ids":["https://openalex.org/I133543626"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075908503","display_name":"Jonah Breslau","orcid":null},"institutions":[{"id":"https://openalex.org/I177881444","display_name":"Pomona College","ror":"https://ror.org/0074grg94","country_code":"US","type":"education","lineage":["https://openalex.org/I177881444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonah Breslau","raw_affiliation_strings":["Department of Mathematics, Pomona College, Claremont, CA 91711"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pomona College, Claremont, CA 91711","institution_ids":["https://openalex.org/I177881444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051160853","display_name":"Daniel Yazdi","orcid":"https://orcid.org/0000-0001-8388-0047"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Yazdi","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015774352","display_name":"Th\u00e9odore Kolokolnikov","orcid":"https://orcid.org/0000-0002-7179-4325"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Theodore Kolokolnikov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003184921","display_name":"Scott G. McCalla","orcid":"https://orcid.org/0000-0003-0093-4658"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott G. McCalla","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5000096589"],"corresponding_institution_ids":["https://openalex.org/I133543626"],"apc_list":null,"apc_paid":null,"fwci":1.647,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.83009813,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"73","issue":"4","first_page":"1703","last_page":"1720"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/l\u00e9vy-flight","display_name":"L\u00e9vy flight","score":0.5291419625282288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.517458975315094},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.5030385851860046},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4800368547439575},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4772357940673828},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.46441930532455444},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4015750586986542},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3025882840156555},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.1218489408493042}],"concepts":[{"id":"https://openalex.org/C118918019","wikidata":"https://www.wikidata.org/wiki/Q4114998","display_name":"L\u00e9vy flight","level":3,"score":0.5291419625282288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.517458975315094},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.5030385851860046},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4800368547439575},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4772357940673828},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.46441930532455444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4015750586986542},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3025882840156555},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.1218489408493042},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120895408","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120895408","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.413.8960","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.8960","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathstat.dal.ca/~tkolokol/papers/levycrime.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1304196372","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G1335286749","display_name":null,"funder_award_id":"W911NF-11-1-03","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2275489661","display_name":null,"funder_award_id":"47050","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5583298662","display_name":"FRG: Collaborative Research: Mathematics of large scale urban crime","funder_award_id":"0968309","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6197249029","display_name":null,"funder_award_id":"W911NF-11-1-0332","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7469649817","display_name":null,"funder_award_id":"W911NF-11-1-0332","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G781543995","display_name":null,"funder_award_id":"1045536","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8353001961","display_name":null,"funder_award_id":"DMS-0968309","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8488940573","display_name":null,"funder_award_id":"DMS-1045536","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G862988727","display_name":null,"funder_award_id":"W911NF-11","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309332","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45"},{"id":"https://openalex.org/F4320321629","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W158120760","https://openalex.org/W249343203","https://openalex.org/W627773405","https://openalex.org/W1570844200","https://openalex.org/W1875318710","https://openalex.org/W1967052442","https://openalex.org/W1978271550","https://openalex.org/W1982300822","https://openalex.org/W1998582544","https://openalex.org/W2007248841","https://openalex.org/W2029107725","https://openalex.org/W2032762515","https://openalex.org/W2040731886","https://openalex.org/W2050274271","https://openalex.org/W2050396090","https://openalex.org/W2056284729","https://openalex.org/W2056583384","https://openalex.org/W2058552802","https://openalex.org/W2063293061","https://openalex.org/W2066686577","https://openalex.org/W2076751494","https://openalex.org/W2098216283","https://openalex.org/W2103741041","https://openalex.org/W2106516566","https://openalex.org/W2117462892","https://openalex.org/W2133286823","https://openalex.org/W2141994409","https://openalex.org/W2145494199","https://openalex.org/W2150330665","https://openalex.org/W2151854755","https://openalex.org/W2155458379","https://openalex.org/W2171547389","https://openalex.org/W2316370367","https://openalex.org/W2325408928","https://openalex.org/W2891585185","https://openalex.org/W3024286765","https://openalex.org/W3126086984"],"related_works":["https://openalex.org/W2742063177","https://openalex.org/W3099019343","https://openalex.org/W1994753018","https://openalex.org/W2386091227","https://openalex.org/W4378214560","https://openalex.org/W2008499310","https://openalex.org/W2026675405","https://openalex.org/W1990590585","https://openalex.org/W1978408548","https://openalex.org/W1974584682"],"abstract_inverted_index":{"The":[0,63,83,185],"UCLA":[1,52],"burglary":[2],"hotspot":[3,219],"model,":[4,102],"introduced":[5],"in":[6,203],"[M.":[7],"B.":[8,14,27],"Short,":[9],"M.":[10],"R.":[11],"D'Orsogna,":[12],"V.":[13],"Pasour,":[15],"G.":[16],"E.":[17],"Tita,":[18],"P.":[19],"J.":[20],"Brantingham,":[21],"A.":[22],"L.":[23,26],"Bertozzi,":[24],"and":[25,113,176],"Chayes,":[28],"Math.":[29],"Models":[30],"Methods":[31],"Appl.":[32],"Sci.,":[33],"18":[34],"(2008),":[35],"pp.":[36],"1249--1267],":[37],"models":[38],"the":[39,51,66,88,115,124,132,140,145,156,159,166,173,178,181,188,200,204,213,217],"formation":[40],"of":[41,43,60,65,87,110,144,158,169,180,187,197,199,216,220],"hotspots":[42],"criminal":[44,67,221],"activity.":[45,222],"In":[46],"this":[47],"paper,":[48],"we":[49,103,210],"extend":[50],"model":[53,59,90,191],"to":[54,79,130,153,194],"incorporate":[55],"a":[56,70,80,95,195],"more":[57],"realistic":[58],"human":[61],"locomotion.":[62],"movement":[64],"agents":[68],"follows":[69],"biased":[71,84],"L\u00e9vy":[72],"flight":[73],"with":[74,99,139],"step":[75],"sizes":[76],"distributed":[77],"according":[78],"power-law":[81],"distribution.":[82],"Brownian":[85],"motion":[86],"original":[89],"is":[91,128,151],"then":[92],"derived":[93],"as":[94,163,165],"special":[96],"case.":[97],"Starting":[98],"an":[100],"agent-based":[101,146,190],"derive":[104],"its":[105],"continuum":[106,133,205],"limit.":[107,206],"This":[108],"consists":[109],"two":[111],"equations":[112],"involves":[114],"fractional":[116],"Laplacian":[117],"operator.":[118],"A":[119,148],"numerical":[120,142],"method":[121],"based":[122],"on":[123,172],"fast":[125],"Fourier":[126],"transform":[127],"used":[129],"simulate":[131],"model;":[134],"these":[135,208],"simulations":[136,143],"compare":[137],"favorably":[138],"direct":[141],"model.":[147],"Turing-type":[149],"analysis":[150],"performed":[152],"estimate":[154],"how":[155],"instability":[157],"homogeneous":[160],"steady":[161],"state,":[162],"well":[164],"expected":[167],"number":[168],"hotspots,":[170],"depends":[171],"system":[174],"parameters":[175],"especially":[177],"exponent":[179],"underlying":[182,189],"power":[183],"law.":[184],"assumptions":[186],"naturally":[192],"lead":[193],"separation":[196],"scales":[198],"diffusion":[201],"coefficients":[202],"Using":[207],"assumptions,":[209],"asymptotically":[211],"construct":[212],"leading-order":[214],"profile":[215],"localized":[218]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}