dc.contributor.author | Corwin, Ivan | |
dc.contributor.author | Quastel, Jeremy | |
dc.contributor.author | Remenik, Daniel | |
dc.date.accessioned | 2016-11-04T20:41:40Z | |
dc.date.available | 2016-11-04T20:41:40Z | |
dc.date.issued | 2015-03 | |
dc.date.submitted | 2015-01 | |
dc.identifier.issn | 0022-4715 | |
dc.identifier.issn | 1572-9613 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/105217 | |
dc.description.abstract | The 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.sponsorship | National Science Foundation (U.S.) (PIRE Grant OISE-07-30136 and DMS-1208998) | en_US |
dc.description.sponsorship | Microsoft Research (Schramm Memorial Fellowship) | en_US |
dc.description.sponsorship | Clay Mathematics Institute (Clay Research Fellowship) | en_US |
dc.description.sponsorship | Institut Henri Poincare (Poincare Chair) | en_US |
dc.description.sponsorship | David & Lucile Packard Foundation (Packard Fellowships for Science and Engineering) Remove selected | en_US |
dc.publisher | Springer US | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s10955-015-1243-8 | en_US |
dc.rights | Article 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.source | Springer US | en_US |
dc.title | Renormalization Fixed Point of the KPZ Universality Class | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Corwin, 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.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Corwin, Ivan | |
dc.relation.journal | Journal of Statistical Physics | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2016-08-18T15:44:38Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer Science+Business Media New York | |
dspace.orderedauthors | Corwin, Ivan; Quastel, Jeremy; Remenik, Daniel | en_US |
dspace.embargo.terms | N | en |
mit.license | PUBLISHER_POLICY | en_US |