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These are: <jats:list list-type=\"order\">\n                \n                  \n                  <jats:list-item>\n                    <jats:p>the vector of critical simplex counts attained by a lexicographical Morse matching,<\/jats:p>\n                  <\/jats:list-item>\n                \n                \n                  \n                  <jats:list-item>\n                    <jats:p>the vector of simplex counts in the link of a fixed simplex, and<\/jats:p>\n                  <\/jats:list-item>\n                \n                \n                  \n                  <jats:list-item>\n                    <jats:p>the vector of total simplex counts.<\/jats:p>\n                  <\/jats:list-item>\n                \n              <\/jats:list> The first of these random vectors forms a cornerstone of modern homology algorithms, while the second one provides a natural generalisation for the notion of vertex degree, and the third one may be viewed from the perspective of <jats:italic>U<\/jats:italic>-statistics. To obtain distributional approximations for these random vectors, we extend the notion of dissociated sums to a multivariate setting and prove a new central limit theorem for such sums using Stein\u2019s method.\n<\/jats:p>","DOI":"10.1007\/s41468-023-00146-5","type":"journal-article","created":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T17:01:46Z","timestamp":1697907706000},"page":"1837-1880","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multivariate central limit theorems for random clique complexes"],"prefix":"10.1007","volume":"8","author":[{"given":"Tadas","family":"Tem\u010dinas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vidit","family":"Nanda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gesine","family":"Reinert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,21]]},"reference":[{"key":"146_CR1","doi-asserted-by":"crossref","unstructured":"Adler, R.J., Bobrowski, O., Weinberger, S.: Crackle: the homology of noise. 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