{"file":[{"file_size":1768663,"file_id":"11742","file_name":"2022_ElecJournCombinatorics_Cooley.pdf","relation":"main_file","date_updated":"2022-08-08T06:28:52Z","date_created":"2022-08-08T06:28:52Z","content_type":"application/pdf","success":1,"access_level":"open_access","creator":"dernst","checksum":"057c676dcee70236aa234d4ce6138c69"}],"publisher":"Electronic Journal of Combinatorics","author":[{"last_name":"Cooley","first_name":"Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","full_name":"Cooley, Oliver"},{"full_name":"Del Giudice, Nicola","first_name":"Nicola","last_name":"Del Giudice"},{"last_name":"Kang","first_name":"Mihyun","full_name":"Kang, Mihyun"},{"full_name":"Sprüssel, Philipp","first_name":"Philipp","last_name":"Sprüssel"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","oa_version":"Published Version","article_number":"P3.27","publication_identifier":{"eissn":["1077-8926"]},"month":"07","article_processing_charge":"No","date_published":"2022-07-29T00:00:00Z","has_accepted_license":"1","publication_status":"published","_id":"11740","publication":"Electronic Journal of Combinatorics","day":"29","status":"public","date_created":"2022-08-07T22:01:59Z","ddc":["510"],"scopus_import":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2005.07103"],"isi":["000836200300001"]},"quality_controlled":"1","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."}],"issue":"3","file_date_updated":"2022-08-08T06:28:52Z","year":"2022","isi":1,"department":[{"_id":"MaKw"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","volume":29,"oa":1,"date_updated":"2023-08-03T12:37:54Z","tmp":{"image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","type":"journal_article","intvolume":"        29","title":"Phase transition in cohomology groups of non-uniform random simplicial complexes","article_type":"original","citation":{"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>.","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>.","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.","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.","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>"},"doi":"10.37236/10607"}