{"author":[{"first_name":"Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","full_name":"Cooley, Oliver","last_name":"Cooley"},{"last_name":"Del Giudice","full_name":"Del Giudice, Nicola","first_name":"Nicola"},{"first_name":"Mihyun","last_name":"Kang","full_name":"Kang, Mihyun"},{"last_name":"Sprüssel","full_name":"Sprüssel, Philipp","first_name":"Philipp"}],"ddc":["510"],"type":"journal_article","article_number":"P3.27","year":"2022","license":"https://creativecommons.org/licenses/by-nd/4.0/","date_created":"2022-08-07T22:01:59Z","month":"07","date_updated":"2023-08-03T12:37:54Z","volume":29,"title":"Phase transition in cohomology groups of non-uniform random simplicial complexes","_id":"11740","department":[{"_id":"MaKw"}],"file":[{"file_name":"2022_ElecJournCombinatorics_Cooley.pdf","file_id":"11742","relation":"main_file","success":1,"date_created":"2022-08-08T06:28:52Z","content_type":"application/pdf","creator":"dernst","date_updated":"2022-08-08T06:28:52Z","file_size":1768663,"checksum":"057c676dcee70236aa234d4ce6138c69","access_level":"open_access"}],"intvolume":"        29","has_accepted_license":"1","oa_version":"Published Version","oa":1,"publication_status":"published","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)"},"isi":1,"acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","date_published":"2022-07-29T00:00:00Z","publication_identifier":{"eissn":["1077-8926"]},"day":"29","status":"public","publication":"Electronic Journal of Combinatorics","quality_controlled":"1","external_id":{"arxiv":["2005.07103"],"isi":["000836200300001"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2022-08-08T06:28:52Z","abstract":[{"text":"We consider a generalised model of a random simplicial complex, which arises from a random hypergraph. Our model is generated by taking the downward-closure of a non-uniform binomial random hypergraph, in which for each k, each set of k+1 vertices forms an edge with some probability pk independently. As a special case, this contains an extensively studied model of a (uniform) random simplicial complex, introduced by Meshulam and Wallach [Random Structures & Algorithms 34 (2009), no. 3, pp. 408–417].\r\nWe consider a higher-dimensional notion of connectedness on this new model according to the vanishing of cohomology groups over an arbitrary abelian group R. We prove that this notion of connectedness displays a phase transition and determine the threshold. We also prove a hitting time result for a natural process interpretation, in which simplices and their downward-closure are added one by one. In addition, we determine the asymptotic behaviour of cohomology groups inside the critical window around the time of the phase transition.","lang":"eng"}],"publisher":"Electronic Journal of Combinatorics","article_processing_charge":"No","issue":"3","language":[{"iso":"eng"}],"citation":{"ama":"Cooley O, Del Giudice N, Kang M, Sprüssel P. Phase transition in cohomology groups of non-uniform random simplicial complexes. <i>Electronic Journal of Combinatorics</i>. 2022;29(3). doi:<a href=\"https://doi.org/10.37236/10607\">10.37236/10607</a>","ieee":"O. Cooley, N. Del Giudice, M. Kang, and P. Sprüssel, “Phase transition in cohomology groups of non-uniform random simplicial complexes,” <i>Electronic Journal of Combinatorics</i>, vol. 29, no. 3. Electronic Journal of Combinatorics, 2022.","chicago":"Cooley, Oliver, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel. “Phase Transition in Cohomology Groups of Non-Uniform Random Simplicial Complexes.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2022. <a href=\"https://doi.org/10.37236/10607\">https://doi.org/10.37236/10607</a>.","mla":"Cooley, Oliver, et al. “Phase Transition in Cohomology Groups of Non-Uniform Random Simplicial Complexes.” <i>Electronic Journal of Combinatorics</i>, vol. 29, no. 3, P3.27, Electronic Journal of Combinatorics, 2022, doi:<a href=\"https://doi.org/10.37236/10607\">10.37236/10607</a>.","ista":"Cooley O, Del Giudice N, Kang M, Sprüssel P. 2022. Phase transition in cohomology groups of non-uniform random simplicial complexes. Electronic Journal of Combinatorics. 29(3), P3.27.","short":"O. Cooley, N. Del Giudice, M. Kang, P. Sprüssel, Electronic Journal of Combinatorics 29 (2022).","apa":"Cooley, O., Del Giudice, N., Kang, M., &#38; Sprüssel, P. (2022). Phase transition in cohomology groups of non-uniform random simplicial complexes. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/10607\">https://doi.org/10.37236/10607</a>"},"doi":"10.37236/10607","scopus_import":"1"}