Law of Large Numbers for Wiener Measure with Density Having Two Large Deviation Minimizers
Tatsushi OTOBE
Source: Tokyo J. of Math.
Volume 32, Number 1
(2009), 279-286.
Abstract
This paper discusses the situation that the large deviation rate functional has two distinct minimizers, for a model described by Wiener measures with certain densities involving a scaling.
The motivation comes from the study of the so-called $\nabla\varphi$ interface model with weak self potentials.
The pinned Wiener measures case was discussed by [3].
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription.
Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tjm/1249648422
Digital Object Identifier: doi:10.3836/tjm/1249648422
Zentralblatt MATH identifier:
05604248
Mathematical Reviews number (MathSciNet):
MR2541167
References
E. Bolthausen, T. Funaki and T. Otobe, Concentration under scaling limits for weakly pinned Gaussian random walks, Probab. Theory Relat. Fields, 143 (2009), 441--480.
T. Funaki, Stochastic Interface Models, in, Lectures on Probability Theory and Statistics, Ecole d'Eté de Probabilités de Saint-Flour XXXIII- -2003, ed. J. Picard, Lect. Notes Math. 1869, Springer, 2005, 103--274.
T. Funaki, Dichotomy in a scaling limit under Wiener measure with density, Electron. Comm. Probab., 12 (2007), 173--183.
T. Funaki and H. Sakagawa, Large deviations for $\nabla\varphi$ interface model and derivation of free boundary problems, Proceedings of Shonan/Kyoto meetings ``Stochastic Analysis on Large Scale Interacting Systems'' (2002, eds. Funaki and Osada), Adv. Stud. Pure Math., 39 Math. Soc. Japan, 2004, 173--211.
I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, (2nd edition), Springer, 1991.
T. Otobe, Large deviations for the $\nabla\varphi$ interface model with self potentials, Proc. Japan Acad. Ser. A, 85 (2009), 31--36.
L. Sirovich, Techniques of Asymptotic Analysis, Applied Mathematical Sciences 2, Springer, 1971.
Mathematical Reviews (MathSciNet):
MR275034
