{"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.","month":"11","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"OA_type":"gold","article_number":"70","oa":1,"ddc":["510"],"doi":"10.1214/24-ECP639","volume":29,"year":"2024","external_id":{"arxiv":["2311.16631"]},"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"publication":"Electronic Communications in Probability","language":[{"iso":"eng"}],"DOAJ_listed":"1","publication_status":"published","publisher":"Duke University Press","title":"Climbing up a random subgraph of the hypercube","date_published":"2024-11-24T00:00:00Z","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","intvolume":"        29","day":"24","department":[{"_id":"MaKw"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2311.16631"}],"status":"public","file_date_updated":"2024-12-16T07:33:34Z","scopus_import":"1","ec_funded":1,"date_updated":"2024-12-16T07:34:09Z","date_created":"2024-12-15T23:01:51Z","type":"journal_article","arxiv":1,"article_type":"original","corr_author":"1","publication_identifier":{"eissn":["1083-589X"]},"has_accepted_license":"1","author":[{"full_name":"Anastos, Michael","first_name":"Michael","last_name":"Anastos","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb"},{"last_name":"Diskin","full_name":"Diskin, Sahar","first_name":"Sahar"},{"full_name":"Elboim, Dor","first_name":"Dor","last_name":"Elboim"},{"first_name":"Michael","full_name":"Krivelevich, Michael","last_name":"Krivelevich"}],"file":[{"date_created":"2024-12-16T07:33:34Z","date_updated":"2024-12-16T07:33:34Z","checksum":"307a9d049325e6ca9bfe8b4a1f275983","file_id":"18657","access_level":"open_access","file_size":530169,"creator":"dernst","content_type":"application/pdf","success":1,"relation":"main_file","file_name":"2024_ElectrCommProbability_Anastos.pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"repository","oa_version":"Published Version","article_processing_charge":"Yes","citation":{"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>.","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>","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>","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.","ista":"Anastos M, Diskin S, Elboim D, Krivelevich M. 2024. Climbing up a random subgraph of the hypercube. Electronic Communications in Probability. 29, 70.","short":"M. Anastos, S. Diskin, D. Elboim, M. Krivelevich, Electronic Communications in Probability 29 (2024)."},"_id":"18655"}