Kardar-Parisi-Zhang universality in first-passage percolation: the role of geodesic degeneracy

dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Interdisciplinar de Sistemas Complejos (GISC)es
dc.contributor.authorCordoba Torres, Pedro
dc.contributor.authorSantalla, Silvia N.
dc.contributor.authorCuerno, Rodolfo
dc.contributor.authorRodríguez Laguna, Javier
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.description.abstractWe have characterized the scaling behavior of the first-passage percolation (FPP) model on two types of discrete networks, the regular square lattice and the disordered Delaunay lattice, thereby addressing the effect of the underlying topology. Several distribution functions for the link-times were considered. The asymptotic behavior of the fluctuations for both the minimal arrival time and the lateral deviation of the geodesic path are in perfect agreement with the Kardar-Parisi-Zhang (KPZ) universality class regardless of the type of the link-time distribution and of the lattice topology. Pre-asymptotic behavior, on the other hand, is found to depend on the uniqueness of geodesics in absence of disorder in the local crossing times, a topological property of lattice directions that we term geodesic degeneracy. This property has important consequences on the model, as for example the well-known anisotropic growth in regular lattices. In this work we provide a framework to understand its effect as well as to characterize its extent.en
dc.description.sponsorshipWe acknowledge fruitful conversations with E. Korutcheva. This work has been supported by MINECO/FEDER (Spain/EU) grants FIS2015-66020-C2-1-P and FIS2015-69167-C2-1-P.en
dc.identifier.bibliographicCitationCórdoba-Torres, P., Santalla, S.N., Cuerno, R. y Rodríguez-Laguna, J. (2018). Kardar-Parisi-Zhang Universality in First-Passage Percolation: the Role of Geodesic Degeneracy. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018(063212)en
dc.identifier.publicationtitleJournal of Statistical Mechanics: Theory and Experimenten
dc.identifier.publicationvolume2018 (063212)
dc.publisherIOP Publishingen
dc.relation.projectIDGobierno de España. FIS2015-66020-C2-1-Pes
dc.relation.projectIDGobierno de España. FIS2015-69167-C2-1-Pes
dc.rights© 2018 IOP Publishing Ltd and SISSA Medialab srl.en
dc.rights.accessRightsopen accessen
dc.subject.otherPercolation problemsen
dc.subject.otherFluctuation phenomenaen
dc.subject.otherInterfaces in random mediaen
dc.subject.otherSelf-affine roughnessen
dc.titleKardar-Parisi-Zhang universality in first-passage percolation: the role of geodesic degeneracyen
dc.typeresearch article*
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
942.48 KB
Adobe Portable Document Format