{"id":"https://openalex.org/W7152578307","doi":"https://doi.org/10.48550/arxiv.2604.07234","title":"The Random Subsequence Model and Uniform Codes for the Deletion Channel","display_name":"The Random Subsequence Model and Uniform Codes for the Deletion Channel","publication_year":2026,"publication_date":"2026-04-08","ids":{"openalex":"https://openalex.org/W7152578307","doi":"https://doi.org/10.48550/arxiv.2604.07234"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07234","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07234","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.07234","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031430372","display_name":"Ryan Jeong","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jeong, Ryan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085988626","display_name":"Francisco Pernice","orcid":"https://orcid.org/0000-0001-6507-8317"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pernice, Francisco","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031430372"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T12029","display_name":"DNA and Biological Computing","score":0.4828999936580658,"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/T12029","display_name":"DNA and Biological Computing","score":0.4828999936580658,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.3012999892234802,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.04439999908208847,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/subsequence","display_name":"Subsequence","score":0.8075000047683716},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.6523000001907349},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4878000020980835},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.45509999990463257},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.4528999924659729},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.44440001249313354},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.41499999165534973},{"id":"https://openalex.org/keywords/longest-common-subsequence-problem","display_name":"Longest common subsequence problem","score":0.40639999508857727}],"concepts":[{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.8075000047683716},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6773999929428101},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.6523000001907349},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6179999709129333},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.45509999990463257},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.4528999924659729},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.44440001249313354},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.41499999165534973},{"id":"https://openalex.org/C120098539","wikidata":"https://www.wikidata.org/wiki/Q141001","display_name":"Longest common subsequence problem","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.384799987077713},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C150775274","wikidata":"https://www.wikidata.org/wiki/Q1490646","display_name":"Spin glass","level":2,"score":0.34860000014305115},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07234","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07234","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.07234","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07234","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.48943057656288147,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,30,62,212],"introduce":[1],"the":[2,34,46,64,75,83,86,104,122,128,133,142,161,178,191,200,207,220,225,232,243,251,255,268,271,284,292,295],"Random":[3,65],"Subsequence":[4,66],"Model,":[5],"a":[6,56,109,153,166,174,237],"spin":[7,154],"glass":[8,155],"model":[9,227],"on":[10,242],"pairs":[11],"of":[12,26,60,97,132,141,190,224,231,270,294],"random":[13,93],"strings":[14],"$(X,Y)":[15],"\\in":[16,114],"\\{0,1\\}^N":[17],"\\times":[18],"\\{0,1\\}^M$":[19],"whose":[20],"partition":[21],"function":[22],"counts":[23],"subsequence":[24,59,89],"embeddings":[25],"$Y$":[27,40,54],"into":[28],"$X$.":[29,61],"study":[31],"two":[32,92],"variants:":[33],"null":[35,123,134],"model,":[36,48],"where":[37,49,106],"$X$":[38,50],"and":[39,43,45,53,95,127,135,195,198,264,288],"are":[41,151,277],"independent":[42],"uniform,":[44],"planted":[47,136,226],"is":[51,55],"uniform":[52,275],"uniformly-random":[57,80,171,248],"length-$M$":[58],"connect":[63],"Model":[67],"to":[68,280],"longstanding":[69],"problems":[70],"in":[71,82,100,152,177,250],"various":[72],"fields,":[73],"including":[74],"best":[76,244,285],"rate":[77,176,204,245],"achievable":[78,246],"by":[79,247],"codes":[81,172,249,276],"deletion":[84,179,183,252,272,296],"channel,":[85,253],"longest":[87],"common":[88],"problem":[90],"between":[91,121],"strings,":[94],"models":[96,137,150],"directed":[98],"polymers":[99],"statistical":[101],"physics.":[102],"In":[103],"regime":[105,208],"$N,M\\to\\infty$":[107],"at":[108,138,157],"fixed":[110],"ratio":[111],"$\u03b1=":[112],"M/N":[113],"(0,1)$,":[115],"we":[116,168],"exhibit":[117],"strict":[118],"asymptotic":[119],"separations":[120],"annealed":[124,221],"free":[125,130,222],"energy":[126,223],"quenched":[129],"energies":[131],"all":[139,182,229],"values":[140,230],"density":[143,233],"parameter":[144],"$\u03b1$.":[145],"This":[146,235],"suggests":[147],"that":[148,170],"these":[149],"phase":[156],"zero":[158],"temperature":[159],"throughout":[160],"entire":[162],"dense":[163],"regime.":[164],"As":[165],"consequence,":[167],"show":[169],"achieve":[173],"positive":[175,203],"channel":[180,273],"for":[181,206,219,228,267,291],"probabilities":[184],"$p\\in":[185],"[0,1),$":[186],"settling":[187],"multiple":[188],"conjectures":[189],"second":[192],"author,":[193],"Isik":[194],"Weissman":[196],"(2024)":[197],"proving":[199],"first":[201,260],"such":[202],"result":[205],"$p":[209],"\\geq":[210],"1/2$.":[211],"also":[213],"give":[214],"an":[215],"exact":[216],"analytic":[217,239],"formula":[218],"parameter.":[234],"implies":[236],"corresponding":[238],"upper":[240,263,287],"bound":[241,257],"complementing":[254],"lower":[256,265,289],"from":[258],"our":[259],"result.":[261],"Our":[262],"bounds":[266,290],"capacity":[269,293],"under":[274],"far":[278],"closer":[279],"each":[281],"other":[282],"than":[283],"known":[286],"channel.":[297]},"counts_by_year":[],"updated_date":"2026-04-10T06:07:51.998497","created_date":"2026-04-10T00:00:00"}
