{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:06:58Z","timestamp":1775052418413,"version":"3.50.1"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T00:00:00Z","timestamp":1583280000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T00:00:00Z","timestamp":1583280000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2020,4]]},"DOI":"10.1007\/s00493-019-3847-0","type":"journal-article","created":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T05:50:56Z","timestamp":1583301056000},"page":"245-281","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["High Order Random Walks: Beyond Spectral Gap"],"prefix":"10.1007","volume":"40","author":[{"given":"Tali","family":"Kaufman","sequence":"first","affiliation":[]},{"given":"Izhar","family":"Oppenheim","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,3,4]]},"reference":[{"key":"3847_CR1","volume-title":"Log-concave polynomials II: High-dimensional walks and an FPRAS for counting bases of a matroid","author":"N Anari","year":"2018","unstructured":"N. Anari, K. Liu, Sh. O. Gharan and C. Vinzant: Log-concave polynomials II: High-dimensional walks and an FPRAS for counting bases of a matroid, arXiv:1811.01816, 2018."},{"key":"3847_CR2","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1137\/130929394","volume":"44","author":"B Barak","year":"2015","unstructured":"B. Barak, P. Gopalan, J. H\u00e5stad, R. Meka, P. Raghavendra and D. Steurer: Making the long code shorter, SIAM J. Comput.44 (2015), 1287\u20131324.","journal-title":"SIAM J. Comput."},{"key":"3847_CR3","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s000390050022","volume":"7","author":"W Ballmann","year":"1997","unstructured":"W. Ballmann and J. \u015awi\u0105tkowski: On L2 -cohomology and property (T) for automorphism groups of polyhedral cell complexes, Geom. Funct. Anal.7 (1997), 615\u2013645.","journal-title":"Geom. Funct. Anal."},{"key":"3847_CR4","volume-title":"Boolean functions on high-dimensional expanders","author":"Y Dikstein","year":"2018","unstructured":"Y. Dikstein, I. Dinur, Y. Filmus and P. Harsha: Boolean functions on high-dimensional expanders, arXiv:1804.08155, 2018."},{"key":"3847_CR5","volume-title":"Electronic Colloquium on Computational Complexity (ECCC)","author":"I Dinur","year":"2017","unstructured":"I. Dinur and T. Kaufman: High dimensional expanders imply agreement expanders, Electronic Colloquium on Computational Complexity (ECCC), 2017."},{"key":"3847_CR6","first-page":"198","volume":"23","author":"I Dinur","year":"2016","unstructured":"I. Dinur, S. Khot, G. Kindler, D. Minzer and M. Safra: Towards a proof of the 2-to-1 games conjecture?, Electronic Colloquium on Computational Complexity (ECCC)23 (2016), 198.","journal-title":"Electronic Colloquium on Computational Complexity (ECCC)"},{"key":"3847_CR7","first-page":"94","volume":"24","author":"I Dinur","year":"2017","unstructured":"I. Dinur, S. Khot, G. Kindler, D. Minzer and M. Safra: On non-optimally expanding sets in grassmann graphs, Electronic Colloquium on Computational Complexity (ECCC)24 (2017), 94.","journal-title":"Electronic Colloquium on Computational Complexity (ECCC)"},{"key":"3847_CR8","doi-asserted-by":"publisher","first-page":"375","DOI":"10.2307\/1970829","volume":"97","author":"H Garland","year":"1973","unstructured":"H. Garland: p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. of Math. (2)97 (1973), 375\u2013423.","journal-title":"Ann. of Math. (2)"},{"key":"3847_CR9","first-page":"151","volume-title":"Computational geometry (SCG\u201912)","author":"A Gundert","year":"2012","unstructured":"A. Gundert and U. Wagner: On Laplacians of random complexes, in: Computational geometry (SCG\u201912), 151\u2013160. ACM, New York, 2012."},{"key":"3847_CR10","volume-title":"ITCS","author":"T Kaufman","year":"2017","unstructured":"T. Kaufman and D. Mass: High dimensional combinatorial random walks and colorful expansion, in: ITCS, 2017."},{"key":"3847_CR11","doi-asserted-by":"publisher","first-page":"67","DOI":"10.4171\/GGD\/306","volume":"9","author":"I Oppenheim","year":"2015","unstructured":"I. Oppenheim: Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes, Groups Geom. Dyn.9 (2015), 67\u2013101.","journal-title":"Groups Geom. Dyn."},{"key":"3847_CR12","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s00454-017-9948-x","volume":"59","author":"I Oppenheim","year":"2018","unstructured":"I. Oppenheim: Local spectral expansion approach to high dimensional expanders Part I: Descent of spectral gaps, Discrete Comput. Geom.59 (2018), 293\u2013330.","journal-title":"Discrete Comput. Geom."}],"updated-by":[{"DOI":"10.1007\/s00493-021-4451-7","type":"erratum","label":"Erratum","source":"publisher","updated":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T00:00:00Z","timestamp":1635292800000}}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-019-3847-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-019-3847-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-019-3847-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T07:04:25Z","timestamp":1635404665000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-019-3847-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,4]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["3847"],"URL":"https:\/\/doi.org\/10.1007\/s00493-019-3847-0","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,4]]},"assertion":[{"value":"7 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 October 2021","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Erratum","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"An Erratum to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s00493-021-4451-7","URL":"https:\/\/doi.org\/10.1007\/s00493-021-4451-7","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}]}}