Nagler, Jan

[["dc.bibliographiccitation.artnumber","052130"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","PHYSICAL REVIEW E"],["dc.bibliographiccitation.volume","87"],["dc.contributor.author","Chen, Wei"],["dc.contributor.author","Nagler, Jan"],["dc.contributor.author","Cheng, Xueqi"],["dc.contributor.author","Jin, Xiaolong"],["dc.contributor.author","Shen, Huawei"],["dc.contributor.author","Zheng, Zhiming"],["dc.contributor.author","D'Souza, Raissa M."],["dc.date.accessioned","2018-11-07T09:24:36Z"],["dc.date.available","2018-11-07T09:24:36Z"],["dc.date.issued","2013"],["dc.description.abstract","Percolation describes the sudden emergence of large-scale connectivity as edges are added to a lattice or random network. In the Bohman-Frieze-Wormald model (BFW) of percolation, edges sampled from a random graph are considered individually and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function with asymptotic value of alpha, a constant. The BFW process has been studied as a model system for investigating the underlying mechanisms leading to discontinuous phase transitions in percolation. Here we focus on the regime alpha is an element of [0.6,0.95] where it is known that only one giant component, denoted C-1, initially appears at the discontinuous phase transition. We show that at some point in the supercritical regime C-1 stops growing and eventually a second giant component, denoted C-2, emerges in a continuous percolation transition. The delay between the emergence of C-1 and C-2 and their asymptotic sizes both depend on the value of a and we establish by several techniques that there exists a bifurcation point alpha(c) = 0.763 +/- 0.002. For a. [0.6, ac), C-1 stops growing the instant it emerges and the delay between the emergence of C-1 and C-2 decreases with increasing alpha. For alpha is an element of (alpha(c), 0.95], in contrast, C-1 continues growing into the supercritical regime and the delay between the emergence of C-1 and C-2 increases with increasing alpha. As we show, alpha(c) marks the minimal delay possible between the emergence of C-1 and C-2 (i.e., the smallest edge density for which C-2 can exist). We also establish many features of the continuous percolation of C-2 including scaling exponents and relations."],["dc.identifier.doi","10.1103/PhysRevE.87.052130"],["dc.identifier.isi","000319393900001"],["dc.identifier.pmid","23767510"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/29864"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1539-3755"],["dc.title","Phase transitions in supercritical explosive percolation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.issue","15"],["dc.bibliographiccitation.journal","Physical Review Letters"],["dc.bibliographiccitation.volume","112"],["dc.contributor.author","Chen, Wei"],["dc.contributor.author","Schroeder, Malte"],["dc.contributor.author","D'Souza, Raissa M."],["dc.contributor.author","Sornette, Didier"],["dc.contributor.author","Nagler, Jan"],["dc.date.accessioned","2018-11-07T09:41:12Z"],["dc.date.available","2018-11-07T09:41:12Z"],["dc.date.issued","2014"],["dc.identifier.doi","10.1103/PhysRevLett.112.155701"],["dc.identifier.isi","000335228000006"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/33676"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1079-7114"],["dc.relation.issn","0031-9007"],["dc.title","Microtransition Cascades to Percolation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","042152"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","PHYSICAL REVIEW E"],["dc.bibliographiccitation.volume","88"],["dc.contributor.author","Chen, Wei"],["dc.contributor.author","Cheng, Xueqi"],["dc.contributor.author","Zheng, Zhiming"],["dc.contributor.author","Chung, Ning Ning"],["dc.contributor.author","D'Souza, Raissa M."],["dc.contributor.author","Nagler, Jan"],["dc.date.accessioned","2018-11-07T09:18:25Z"],["dc.date.available","2018-11-07T09:18:25Z"],["dc.date.issued","2013"],["dc.description.abstract","The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the addition of a single edge causes the size of the largest component to exhibit a significant macroscopic jump in the thermodynamic limit. These processes can have additional exotic behaviors, such as displaying a \"Devil's staircase\" of discrete jumps in the supercritical regime. Here we investigate whether the location of the largest jump coincides with the percolation threshold for a range of processes, such as Erdos-Renyipercolation, percolation via edge competition and via growth by overtaking. We find that the largest jump asymptotically occurs at the percolation transition for Erdos-Renyiand other processes exhibiting global continuity, including models exhibiting an \"explosive\" transition. However, for percolation processes exhibiting genuine discontinuities, the behavior is substantially richer. In percolation models where the order parameter exhibits a staircase, the largest discontinuity generically does not coincide with the percolation transition. For the generalized Bohman-Frieze-Wormald model, it depends on the model parameter. Distinct parameter regimes well in the supercritical regime feature unstable discontinuous transitions-a novel and unexpected phenomenon in percolation. We thus demonstrate that seemingly and genuinely discontinuous percolation transitions can involve a rich behavior in supercriticality, a regime that has been largely ignored in percolation."],["dc.identifier.doi","10.1103/PhysRevE.88.042152"],["dc.identifier.isi","000326392300003"],["dc.identifier.pmid","24229160"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/28406"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1550-2376"],["dc.relation.issn","1539-3755"],["dc.title","Unstable supercritical discontinuous percolation transitions"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]