{"id":"https://openalex.org/W7204155814","doi":"https://doi.org/10.48550/arxiv.2608.23401","title":"Extreme values and logarithm laws for toral translations","display_name":"Extreme values and logarithm laws for toral translations","publication_year":2026,"publication_date":"2026-08-24","ids":{"openalex":"https://openalex.org/W7204155814","doi":"https://doi.org/10.48550/arxiv.2608.23401"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.23401","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23401","pdf_url":"https://arxiv.org/pdf/2608.23401","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-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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/2608.23401","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101969699","display_name":"SOURAV DAS","orcid":"https://orcid.org/0000-0002-2547-7089","observed_orcids":["https://orcid.org/0000-0002-2547-7089"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Das, Sourav","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112010532","display_name":"Anish Ghosh","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ghosh, Anish","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148155616","display_name":"Sundara Narasimhan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Narasimhan, Sundara","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.9467999935150146,"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":0.9467999935150146,"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/T11166","display_name":"Analytic Number Theory Research","score":0.02810000069439411,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.001500000013038516,"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/logarithm-laws","display_name":"logarithm laws","score":0.9470000267028809},{"id":"https://openalex.org/keywords/inhomogeneous-diophantine-approximation","display_name":"inhomogeneous Diophantine approximation","score":0.9350000023841858},{"id":"https://openalex.org/keywords/nearest-neighbor-distance","display_name":"nearest neighbor distance","score":0.6129999756813049},{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.8949999809265137},{"id":"https://openalex.org/keywords/frechet-distribution","display_name":"Fr\u00e9chet distribution","score":0.9990000128746033},{"id":"https://openalex.org/keywords/homogeneous-dynamics","display_name":"homogeneous dynamics","score":0.9319999814033508},{"id":"https://openalex.org/keywords/poisson-approximation","display_name":"Poisson approximation","score":0.8349999785423279},{"id":"https://openalex.org/keywords/diophantine-condition","display_name":"Diophantine conditions","score":0.8080000281333923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8604999780654907},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.7875000238418579},{"id":"https://openalex.org/C130594498","wikidata":"https://www.wikidata.org/wiki/Q2028293","display_name":"Iterated logarithm","level":3,"score":0.730400025844574},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6955000162124634},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6315000057220459},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.609499990940094},{"id":"https://openalex.org/C102966492","wikidata":"https://www.wikidata.org/wiki/Q1227061","display_name":"Diophantine approximation","level":3,"score":0.5931000113487244},{"id":"https://openalex.org/C139907963","wikidata":"https://www.wikidata.org/wiki/Q198740","display_name":"Law of the iterated logarithm","level":3,"score":0.4645000100135803},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4253999888896942},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4156999886035919},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41530001163482666},{"id":"https://openalex.org/C56017942","wikidata":"https://www.wikidata.org/wiki/Q204037","display_name":"Natural logarithm","level":3,"score":0.4083000123500824},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.3822000026702881},{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34470000863075256},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3285999894142151},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3009999990463257},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26649999618530273},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2513999938964844},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.23401","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23401","pdf_url":"https://arxiv.org/pdf/2608.23401","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-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.23401","doi":"https://doi.org/10.48550/arxiv.2608.23401","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.23401","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-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.23401","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23401","pdf_url":"https://arxiv.org/pdf/2608.23401","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-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204155814.pdf","grobid_xml":"https://content.openalex.org/works/W7204155814.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4410978014","https://openalex.org/W7160094786","https://openalex.org/W7170153490"],"related_works":["https://openalex.org/W7213940288","https://openalex.org/W4299543736","https://openalex.org/W2734087502","https://openalex.org/W4415456065","https://openalex.org/W7214949361","https://openalex.org/W1642963221","https://openalex.org/W7138400398","https://openalex.org/W2166696411","https://openalex.org/W4388951755","https://openalex.org/W4394668021"],"abstract_inverted_index":{"We":[0,53],"study":[1],"extreme":[2,35],"values":[3],"of":[4,59,76,80],"normalised":[5],"$r$-th":[6],"nearest":[7],"neighbour":[8],"distance":[9],"functions":[10,24],"in":[11],"inhomogeneous":[12],"Diophantine":[13,31],"approximation,":[14],"and":[15,18,61,79,82],"prove":[16,39],"Weibull":[17],"Fr\u00e9chet":[19],"limit":[20],"laws":[21,37,42],"for":[22,43],"these":[23,34,44],"when":[25],"the":[26,55],"shift":[27],"satisfies":[28],"a":[29],"natural":[30],"condition.":[32],"Using":[33],"value":[36],"we":[38,72],"corresponding":[40],"logarithm":[41],"functions.":[45],"Our":[46],"approach":[47],"is":[48],"based":[49],"on":[50],"homogeneous":[51],"dynamics.":[52],"adapt":[54],"Poisson":[56],"approximation":[57],"strategy":[58],"Bj$\\ddot{\\text{o}}$rklund":[60],"Gorodnik":[62,83],"(arXiv:2201.05116)":[63],"combined":[64],"with":[65],"an":[66],"effective":[67],"multiple":[68],"equidistribution":[69],"result,":[70],"which":[71],"deduce":[73],"using":[74],"results":[75],"Str$\\ddot{\\text{o}}$mbergsson":[77],"(arXiv:1309.6103)":[78],"Bj\u00f6rklund":[81],"(arXiv:2105.05468).":[84]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-26T00:00:00"}