{"abstract":[{"lang":"eng","text":"Let Qd be the d-dimensional binary hypercube. We say that P={v1,…,vk} is an increasing path of length k−1 in Qd, if for every i∈[k−1] the edge vivi+1 is obtained by switching some zero coordinate in vi to a one coordinate in vi+1.\r\nForm a random subgraph Qdp by retaining each edge in E(Qd) independently with probability p. We show that there is a phase transition with respect to the length of a longest increasing path around p=ed. Let α be a constant and let p=αd. When α<e, then there exists a δ∈[0,1) such that whp a longest increasing path in Qdp is of length at most δd. On the other hand, when α>e, whp there is a path of length d−2 in Qdp, and in fact, whether it is of length d−2,d−1, or d depends on whether the all-zero and all-one vertices percolate or not."}],"scopus_import":"1","file":[{"file_size":530169,"relation":"main_file","checksum":"307a9d049325e6ca9bfe8b4a1f275983","file_name":"2024_ElectrCommProbability_Anastos.pdf","access_level":"open_access","success":1,"creator":"dernst","content_type":"application/pdf","date_updated":"2024-12-16T07:33:34Z","date_created":"2024-12-16T07:33:34Z","file_id":"18657"}],"article_processing_charge":"Yes","OA_type":"gold","corr_author":"1","oa":1,"author":[{"full_name":"Anastos, Michael","first_name":"Michael","last_name":"Anastos","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb"},{"last_name":"Diskin","first_name":"Sahar","full_name":"Diskin, Sahar"},{"first_name":"Dor","full_name":"Elboim, Dor","last_name":"Elboim"},{"first_name":"Michael","full_name":"Krivelevich, Michael","last_name":"Krivelevich"}],"external_id":{"arxiv":["2311.16631"]},"article_number":"70","volume":29,"publication_status":"published","publication_identifier":{"eissn":["1083-589X"]},"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publisher":"Duke University Press","file_date_updated":"2024-12-16T07:33:34Z","doi":"10.1214/24-ECP639","license":"https://creativecommons.org/licenses/by/4.0/","date_updated":"2024-12-16T07:34:09Z","month":"11","department":[{"_id":"MaKw"}],"day":"24","title":"Climbing up a random subgraph of the hypercube","year":"2024","language":[{"iso":"eng"}],"acknowledgement":"Research supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101034413.\r\nThe authors wish to thank Ross Pinsky for his comments on an earlier version of the paper, and for bringing reference [12] to our attention. The authors are grateful to the anonymous referees for their helpful comments and suggestions.","publication":"Electronic Communications in Probability","date_published":"2024-11-24T00:00:00Z","arxiv":1,"OA_place":"repository","DOAJ_listed":"1","quality_controlled":"1","status":"public","project":[{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","ddc":["510"],"article_type":"original","has_accepted_license":"1","date_created":"2024-12-15T23:01:51Z","citation":{"ista":"Anastos M, Diskin S, Elboim D, Krivelevich M. 2024. Climbing up a random subgraph of the hypercube. Electronic Communications in Probability. 29, 70.","apa":"Anastos, M., Diskin, S., Elboim, D., &#38; Krivelevich, M. (2024). Climbing up a random subgraph of the hypercube. <i>Electronic Communications in Probability</i>. Duke University Press. <a href=\"https://doi.org/10.1214/24-ECP639\">https://doi.org/10.1214/24-ECP639</a>","short":"M. Anastos, S. Diskin, D. Elboim, M. Krivelevich, Electronic Communications in Probability 29 (2024).","ieee":"M. Anastos, S. Diskin, D. Elboim, and M. Krivelevich, “Climbing up a random subgraph of the hypercube,” <i>Electronic Communications in Probability</i>, vol. 29. Duke University Press, 2024.","mla":"Anastos, Michael, et al. “Climbing up a Random Subgraph of the Hypercube.” <i>Electronic Communications in Probability</i>, vol. 29, 70, Duke University Press, 2024, doi:<a href=\"https://doi.org/10.1214/24-ECP639\">10.1214/24-ECP639</a>.","ama":"Anastos M, Diskin S, Elboim D, Krivelevich M. Climbing up a random subgraph of the hypercube. <i>Electronic Communications in Probability</i>. 2024;29. doi:<a href=\"https://doi.org/10.1214/24-ECP639\">10.1214/24-ECP639</a>","chicago":"Anastos, Michael, Sahar Diskin, Dor Elboim, and Michael Krivelevich. “Climbing up a Random Subgraph of the Hypercube.” <i>Electronic Communications in Probability</i>. Duke University Press, 2024. <a href=\"https://doi.org/10.1214/24-ECP639\">https://doi.org/10.1214/24-ECP639</a>."},"ec_funded":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2311.16631","open_access":"1"}],"oa_version":"Published Version","_id":"18655","intvolume":"        29"}