Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
The Annals of probability, 2011-01, Vol.39 (1), p.176-223
2011

Details

Autor(en) / Beteiligte
Titel
QUENCHED SCALING LIMITS OF TRAP MODELS
Ist Teil von
  • The Annals of probability, 2011-01, Vol.39 (1), p.176-223
Ort / Verlag
Cleveland, OH: Institute of Mathematical Statistics
Erscheinungsjahr
2011
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
  • In this paper, we study Bouchaud's trap model on the discrete d-dimensional torus ${\Bbb T}_{n}^{d}=({\Bbb Z}/n{\Bbb Z})^{d}$ . In this process, a particle performs a symmetric simple random walk, which waits at the site $x\in {\Bbb T}_{n}^{d}$ an exponential time with mean ξₓ, where $\{\xi _{x},x\in {\Bbb T}_{n}^{d}\}$ is a realization of an i.i.d. sequence of positive random variables with an α-stable law. Intuitively speaking, the value of ξₓ gives the depth of the trap at x. In dimension d = 1, we prove that a system of independent particles with the dynamics described above has a hydrodynamic limit, which is given by the degenerate diffusion equation introduced in [Ann. Probab. 30 (2002) 579–604]. In dimensions d > 1, we prove that the evolution of a single particle is metastable in the sense of Beltrán and Landim [Tunneling and Metastability of continuous time Markov chains (2009) Preprint]. Moreover, we prove that in the ergodic scaling, the limiting process is given by the K-process, introduced by Fontes and Mathieu in [Ann. Probab. 36 (2008) 1322–1358].

Weiterführende Literatur

Empfehlungen zum selben Thema automatisch vorgeschlagen von bX