?url_ver=Z39.88-2004&rft_id=arXiv%3A1711.04273&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F4040%2F&rft.title=Covariance+structure+behind+breaking+of+ensemble+equivalence+in+random+graphs&rft.creator=Garlaschelli%2C+Diego&rft.creator=den+Hollander%2C+Frank&rft.creator=Roccaverde%2C+Andrea&rft.subject=QC+Physics&rft.description=For+a+random+graph+subject+to+a+topological+constraint%2C+the+microcanonical+ensemble+requires+the+constraint+to+be+met+by+every+realisation+of+the+graph+(%60hard+constraint%26%2339%3B)%2C+while+the+canonical+ensemble+requires+the+constraint+to+be+met+only+on+average+(%60soft+constraint%26%2339%3B).+It+is+known+that+breaking+of+ensemble+equivalence+may+occur+when+the+size+of+the+random+graph+tends+to+infinity%2C+signalled+by+a+non-zero+specific+relative+entropy+of+the+two+ensembles.+In+this+paper+we+analyse+a+formula+for+the+relative+entropy+of+generic+random+discrete+structures+recently+put+forward+by+Squartini+and+Garlaschelli.+We+consider+the+case+of+random+graphs+with+given+degree+sequence+(configuration+model)+and+show+that+this+formula+correctly+predicts+that+the+specific+relative+entropy+in+the+dense+regime+is+determined+by+the+matrix+of+canonical+covariances+of+the+constraints.+The+formula+also+correctly+predicts+that+an+extra+correction+term+is+required+in+the+sparse+regime+and+the+ultra-dense+regime.+We+further+show+that+the+different+expressions+correspond+to+the+degrees+in+the+canonical+ensemble+being+asymptotically+Gaussian+in+the+dense+regime+and+asymptotically+Poisson+in+the+sparse+and+the+ultra-dense+regime%2C+as+we+found+in+earlier+work.+In+general%2C+we+show+that+the+degrees+follow+a+multivariate+version+of+the+Poisson-+Binomial+distribution+in+the+canonical+ensemble.&rft.publisher=arXiv&rft.date=2017&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F4040%2F1%2F1711.04273.pdf&rft.identifier=++Garlaschelli%2C+Diego+and+den+Hollander%2C+Frank+and+Roccaverde%2C+Andrea++Covariance+structure+behind+breaking+of+ensemble+equivalence+in+random+graphs.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fpdf%2F1711.04273.pdf&rft.relation=arXiv%3A1711.04273