{"date_updated":"2024-10-09T21:03:03Z","type":"journal_article","oa_version":"Published Version","arxiv":1,"article_processing_charge":"No","date_published":"2022-07-29T00:00:00Z","publication":"Electronic Journal of Combinatorics","file":[{"file_size":1768663,"success":1,"content_type":"application/pdf","file_id":"11742","relation":"main_file","date_created":"2022-08-08T06:28:52Z","access_level":"open_access","creator":"dernst","date_updated":"2022-08-08T06:28:52Z","file_name":"2022_ElecJournCombinatorics_Cooley.pdf","checksum":"057c676dcee70236aa234d4ce6138c69"}],"title":"Phase transition in cohomology groups of non-uniform random simplicial complexes","doi":"10.37236/10607","author":[{"last_name":"Cooley","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","full_name":"Cooley, Oliver","first_name":"Oliver"},{"last_name":"Del Giudice","full_name":"Del Giudice, Nicola","first_name":"Nicola"},{"last_name":"Kang","first_name":"Mihyun","full_name":"Kang, Mihyun"},{"last_name":"Sprüssel","first_name":"Philipp","full_name":"Sprüssel, Philipp"}],"day":"29","acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","file_date_updated":"2022-08-08T06:28:52Z","abstract":[{"lang":"eng","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."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","has_accepted_license":"1","date_created":"2022-08-07T22:01:59Z","_id":"11740","publication_identifier":{"eissn":["1077-8926"]},"year":"2022","ddc":["510"],"scopus_import":"1","publication_status":"published","quality_controlled":"1","language":[{"iso":"eng"}],"isi":1,"tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"license":"https://creativecommons.org/licenses/by-nd/4.0/","department":[{"_id":"MaKw"}],"article_type":"original","corr_author":"1","issue":"3","month":"07","oa":1,"intvolume":"        29","publisher":"Electronic Journal of Combinatorics","volume":29,"status":"public","external_id":{"isi":["000836200300001"],"arxiv":["2005.07103"]},"citation":{"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>.","short":"O. Cooley, N. Del Giudice, M. Kang, P. Sprüssel, Electronic Journal of Combinatorics 29 (2022).","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.","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>","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>"},"article_number":"P3.27"}