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dc.contributor.authorCorwin, Ivan
dc.contributor.authorQuastel, Jeremy
dc.contributor.authorRemenik, Daniel
dc.date.accessioned2016-11-04T20:41:40Z
dc.date.available2016-11-04T20:41:40Z
dc.date.issued2015-03
dc.date.submitted2015-01
dc.identifier.issn0022-4715
dc.identifier.issn1572-9613
dc.identifier.urihttp://hdl.handle.net/1721.1/105217
dc.description.abstractThe one dimensional Kardar–Parisi–Zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents. These exponents lead to a natural renormalization/rescaling on the space of such evolving interfaces. We introduce and describe the renormalization fixed point of the Kardar–Parisi–Zhang universality class in terms of a random nonlinear semigroup with stationary independent increments, and via a variational formula. Furthermore, we compute a plausible formula the exact transition probabilities using replica Bethe ansatz. The semigroup is constructed from the Airy sheet, a four parameter space-time field which is the Airy[subscript 2] process in each of its two spatial coordinates. Minimizing paths through this field describe the renormalization group fixed point of directed polymers in a random potential. At present, the results we provide do not have mathematically rigorous proofs, and they should at most be considered proposals.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (PIRE Grant OISE-07-30136 and DMS-1208998)en_US
dc.description.sponsorshipMicrosoft Research (Schramm Memorial Fellowship)en_US
dc.description.sponsorshipClay Mathematics Institute (Clay Research Fellowship)en_US
dc.description.sponsorshipInstitut Henri Poincare (Poincare Chair)en_US
dc.description.sponsorshipDavid & Lucile Packard Foundation (Packard Fellowships for Science and Engineering) Remove selecteden_US
dc.publisherSpringer USen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s10955-015-1243-8en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer USen_US
dc.titleRenormalization Fixed Point of the KPZ Universality Classen_US
dc.typeArticleen_US
dc.identifier.citationCorwin, Ivan, Jeremy Quastel, and Daniel Remenik. “Renormalization Fixed Point of the KPZ Universality Class.” Journal of Statistical Physics 160.4 (2015): 815–834.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorCorwin, Ivan
dc.relation.journalJournal of Statistical Physicsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-08-18T15:44:38Z
dc.language.rfc3066en
dc.rights.holderSpringer Science+Business Media New York
dspace.orderedauthorsCorwin, Ivan; Quastel, Jeremy; Remenik, Danielen_US
dspace.embargo.termsNen
mit.licensePUBLISHER_POLICYen_US


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