Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 12 (2007), paper no. 18, 173-183.
Dichotomy in a scaling limit under Wiener measure with density
In general, if the large deviation principle holds for a sequence of probability measures and its rate functional admits a unique minimizer, then the measures asymptotically concentrate in its neighborhood so that the law of large numbers follows. This paper discusses the situation that the rate functional has two distinct minimizers, for a simple model described by the pinned Wiener measures with certain densities involving a scaling. We study their asymptotic behavior and determine to which minimizers they converge based on a more precise investigation than the large deviation's level.
Electron. Commun. Probab., Volume 12 (2007), paper no. 18, 173-183.
Accepted: 16 May 2007
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F10: Large deviations
Secondary: 82B24: Interface problems; diffusion-limited aggregation 82B31: Stochastic methods
This work is licensed under aCreative Commons Attribution 3.0 License.
Funaki, Tadahisa. Dichotomy in a scaling limit under Wiener measure with density. Electron. Commun. Probab. 12 (2007), paper no. 18, 173--183. doi:10.1214/ECP.v12-1271. https://projecteuclid.org/euclid.ecp/1465224961