粒子系統的大離差行為

Large Deviations from the Hydrodynamic Limit of the Generalized Symmetric Exclusion Process

林軒馳(Hsuan-Chih Lin)

指導教授 ： 張志中

國立臺灣大學/理學院/數學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.00857

摘要

在這篇文章中，我們研究對稱交互作用粒子系統的大離差行為。
Kipnis, et al.於1994年將導出一般性簡單對稱互斥過程流力極限的行為，本篇文章研究此互斥過程流力極限的大離差行為。

關鍵字

交互作用粒子系統 ； 大離差行為

並列摘要

In the present article, we study the large deviation property of the generalized symmetric exclusion process.
Once the hydrodynamic limit, which corresponds to a space-time law of large numbers type result, of a Markov process has been established, a natural step is to consider the large deviations from the limit.
Kipnis, et al. derived the hydrodynamic limit of a generalized symmetric exclusion process, which is a non-gradient system. We then derive the large deviation principle of this model.

並列關鍵字

Large Deviation ； Hydrodynamic Limit ； Generalized Symmetric Exclusion Process

參考文獻

[1] C, Kipnis, S. Olla, S.R.S Varadhan, Hydrodynamics and large deviations

for simple exclusion process. Comm. Pure Appl. Math., 42

[2] M.D. Donsker, S.R.S. Varadhan, Large deviations from a hydrodynamic

scaling limit. Comm. Pure Appl. Math., 42 (1989), 243-270.

[3] S.R.S. Varadhan, Nonlinear diffusion limit for a system with nearest