{"id":"https://openalex.org/W7220936548","doi":"https://doi.org/10.48550/arxiv.2610.08465","title":"Dimension properties of a family of random self-similar iterated function systems","display_name":"Dimension properties of a family of random self-similar iterated function systems","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220936548","doi":"https://doi.org/10.48550/arxiv.2610.08465"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08465","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08465","pdf_url":"https://arxiv.org/pdf/2610.08465","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08465","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019989875","display_name":"Vilma Orgov\u00e1nyi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Orgov\u00e1nyi, Vilma","raw_affiliation_strings":["Department of Stochastics , Institute of Mathematics , Budapest University of Technology and Economics , M\u0171egyetem rkp. 3 , H-1111 Budapest , Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Stochastics , Institute of Mathematics , Budapest University of Technology and Economics , M\u0171egyetem rkp. 3 , H-1111 Budapest , Hungary","institution_ids":["https://openalex.org/I29770179"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082639384","display_name":"K\u00e1roly Simon","orcid":"https://orcid.org/0000-0003-2397-3828","observed_orcids":["https://orcid.org/0000-0003-2397-3828"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simon, K\u00e1roly","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.00039999998989515007,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.00019999999494757503,"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/iterated-function-systems","display_name":"iterated function systems","score":0.9929999709129333},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.7990000247955322},{"id":"https://openalex.org/keywords/dimension-formula","display_name":"dimension formula","score":0.7829999923706055},{"id":"https://openalex.org/keywords/galton-watson-trees","display_name":"Galton-Watson trees","score":0.7680000066757202},{"id":"https://openalex.org/keywords/pressure-function","display_name":"pressure function","score":0.9020000100135803},{"id":"https://openalex.org/keywords/overlapping-structures","display_name":"overlapping structures","score":0.5630000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8220999836921692},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6601999998092651},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.6003000140190125},{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.5914000272750854},{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.5716999769210815},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.483599990606308},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4277999997138977},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.421999990940094},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.4074999988079071},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3718000054359436},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3513999879360199},{"id":"https://openalex.org/C2776839635","wikidata":"https://www.wikidata.org/wiki/Q14942679","display_name":"Random tree","level":4,"score":0.3328999876976013},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C13929819","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Random function","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C67499762","wikidata":"https://www.wikidata.org/wiki/Q4943358","display_name":"Boolean model","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C15867958","wikidata":"https://www.wikidata.org/wiki/Q5280413","display_name":"Directed percolation","level":4,"score":0.2590999901294708},{"id":"https://openalex.org/C139907963","wikidata":"https://www.wikidata.org/wiki/Q198740","display_name":"Law of the iterated logarithm","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08465","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08465","pdf_url":"https://arxiv.org/pdf/2610.08465","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.08465","doi":"https://doi.org/10.48550/arxiv.2610.08465","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08465","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08465","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08465","pdf_url":"https://arxiv.org/pdf/2610.08465","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2774216544","display_name":null,"funder_award_id":"K142169","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G4042934884","display_name":null,"funder_award_id":"KKP144059","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G8528715892","display_name":null,"funder_award_id":"FK134251","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"}],"funders":[{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220936548.pdf","grobid_xml":"https://content.openalex.org/works/W7220936548.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W121824094","https://openalex.org/W1970155913","https://openalex.org/W1997287185","https://openalex.org/W2021372958","https://openalex.org/W2025127707","https://openalex.org/W2035081222","https://openalex.org/W2041024520","https://openalex.org/W2048573155","https://openalex.org/W2084337755","https://openalex.org/W2133577993","https://openalex.org/W2143590429","https://openalex.org/W2211277762","https://openalex.org/W2243303474","https://openalex.org/W2331369044","https://openalex.org/W2953325590","https://openalex.org/W4231110773","https://openalex.org/W4388093908","https://openalex.org/W4401387128","https://openalex.org/W7131672972"],"related_works":["https://openalex.org/W4416508759","https://openalex.org/W1553550627","https://openalex.org/W2753895334","https://openalex.org/W3098741874","https://openalex.org/W942342895","https://openalex.org/W2745628349","https://openalex.org/W2886947241","https://openalex.org/W775480254","https://openalex.org/W1979475101","https://openalex.org/W2954684797"],"abstract_inverted_index":{"In":[0],"this":[1],"note":[2],"we":[3,16],"present":[4],"a":[5,45,75],"dimension":[6,68],"formula":[7,69],"for":[8,56],"certain":[9],"randomized":[10],"self-similar":[11,14],"sets.":[12],"The":[13,40,67],"sets":[15],"are":[17,19],"considering":[18],"$d$-dimensional":[20],"generalizations":[21],"of":[22,25,53,62,74,91],"rational":[23],"projections":[24],"inhomogeneous":[26],"sponges:":[27],"they":[28],"have":[29],"overlaps,":[30],"but":[31],"the":[32,51,54,60,63,80,85,89,92],"overlapping":[33,86],"structure":[34,87],"is":[35,70],"in":[36,59,72],"some":[37],"sense":[38],"well-organized.":[39],"randomization":[41],"happens":[42],"according":[43],"to":[44,50,79],"labelled":[46],"Galton-Watson":[47],"tree":[48],"corresponding":[49,78],"cylinders":[52],"IFS,":[55],"example":[57],"as":[58],"case":[61],"Mandelbrot":[64],"percolation":[65],"set.":[66],"given":[71],"terms":[73],"pressure":[76],"function":[77],"expectation":[81],"matrices,":[82],"which":[83],"describes":[84],"and":[88],"randomness":[90],"system.":[93]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}