## Electronic Communications in Probability

### Dichotomy in a scaling limit under Wiener measure with density

#### Abstract

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.

#### Article information

Source
Electron. Commun. Probab., Volume 12 (2007), paper no. 18, 173-183.

Dates
Accepted: 16 May 2007
First available in Project Euclid: 6 June 2016

https://projecteuclid.org/euclid.ecp/1465224961

Digital Object Identifier
doi:10.1214/ECP.v12-1271

Mathematical Reviews number (MathSciNet)
MR2318164

Zentralblatt MATH identifier
1128.60021

Subjects
Primary: 60F10: Large deviations
Secondary: 82B24: Interface problems; diffusion-limited aggregation 82B31: Stochastic methods

Rights

#### Citation

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

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