## 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

#### 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

**Permanent link to this document**

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

**Keywords**

Large deviation principle minimizers pinned Wiener measure scaling limit concentration

**Rights**

This work is licensed under aCreative Commons Attribution 3.0 License.

#### 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