Disorder relevance for the random walk pinning model in dimension 3
- Publikationstyp:
- Zeitschriftenaufsatz
- Metadaten:
-
- Autoren
- Matthias Birkner
- Rongfeng Sun
- Autoren-URL
- https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000286788800013&DestLinkType=FullRecord&DestApp=WOS_CPL
- DOI
- 10.1214/10-AIHP374
- Externe Identifier
- Clarivate Analytics Document Solution ID: 714DX
- ISSN
- 0246-0203
- Ausgabe der Veröffentlichung
- 1
- Zeitschrift
- ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
- Schlüsselwörter
- Collision local time
- Disordered pinning models
- Fractional moment method
- Local limit theorem
- Marginal disorder
- Random walks
- Renewal processes with infinite mean
- Paginierung
- 259 - 293
- Datum der Veröffentlichung
- 2011
- Status
- Published
- Titel
- Disorder relevance for the random walk pinning model in dimension 3
- Sub types
- Article
- Ausgabe der Zeitschrift
- 47
Datenquelle: Web of Science (Lite)
- Andere Metadatenquellen:
-
- Autoren
- Matthias Birkner
- Rongfeng Sun
- DOI
- 10.1214/10-aihp374
- ISSN
- 0246-0203
- Ausgabe der Veröffentlichung
- 1
- Zeitschrift
- Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
- Datum der Veröffentlichung
- 2011
- Status
- Published
- Herausgeber
- Institute of Mathematical Statistics
- Herausgeber URL
- http://dx.doi.org/10.1214/10-aihp374
- Datum der Datenerfassung
- 2021
- Titel
- Disorder relevance for the random walk pinning model in dimension 3
- Ausgabe der Zeitschrift
- 47
Datenquelle: Crossref
- Abstract
- We study the continuous time version of the random walk pinning model, where conditioned on a continuous time random walk Y on Z^d with jump rate \rho>0, which plays the role of disorder, the law up to time t of a second independent random walk X with jump rate 1 is Gibbs transformed with weight e^{\beta L_t(X,Y)}, where L_t(X,Y) is the collision local time between X and Y up to time t. As the inverse temperature \beta varies, the model undergoes a localization-delocalization transition at some critical \beta_c>=0. A natural question is whether or not there is disorder relevance, namely whether or not \beta_c differs from the critical point \beta_c^{ann} for the annealed model. In Birkner and Sun [BS09], it was shown that there is disorder irrelevance in dimensions d=1 and 2, and disorder relevance in d>=4. For d>=5, disorder relevance was first proved by Birkner, Greven and den Hollander [BGdH08]. In this paper, we prove that if X and Y have the same jump probability kernel, which is irreducible and symmetric with finite second moments, then there is also disorder relevance in the critical dimension d=3, and \beta_c-\beta^{ann}_c is at least of the order e^{-C(\zeta)\rho^{-\zeta}}, C(\zeta)>0, for any \zeta>2. Our proof employs coarse graining and fractional moment techniques, which have recently been applied by Lacoin [L09] to the directed polymer model in random environment, and by Giacomin, Lacoin and Toninelli [GLT09] to establish disorder relevance for the random pinning model in the critical dimension. Along the way, we also prove a continuous time version of Doney's local limit theorem [D97] for renewal processes with infinite mean.
- Autoren
- Matthias Birkner
- Rongfeng Sun
- Autoren-URL
- http://arxiv.org/abs/0912.1663v3
- Schlüsselwörter
- math.PR
- math.PR
- 60K35, 82B44
- Notes
- 36 pages, revised version following referee's comments. Change of title. Added a monotonicity result (Theorem 1.3) on the critical point shift shown to us by the referee.
- Datum der Veröffentlichung
- 2009
- Datum der Datenerfassung
- 2009
- Datum, an dem der Datensatz öffentlich gemacht wurde
- 2009
- Titel
- Disorder relevance for the random walk pinning model in dimension 3
Files
0912.1663v3.pdf
Datenquelle: arXiv
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