張志中臺灣大學：數學研究所林軒馳Lin, Hsuan-ChihHsuan-ChihLin2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/59463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。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.口試委員會審定書……………………………………………… i 誌謝………… …………………………………………………… ii 中文摘要………………………………………………… iii 英文摘要…………………………………………………………… iv 1. Introduction ……………………………………………… 1 2. Notation and Results ………………………………… …… 1 3. Upper Bound ………………………………………………… 5 4. Hydrodynamic Limit for a Weakly Perturbed Process …12 5. Lower Bound ……………………………………………………17 參考文獻…………………………………………………………… 19343407 bytesapplication/pdfen-US交互作用粒子系統大離差行為Large DeviationHydrodynamic LimitGeneralized Symmetric Exclusion Processthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59463/1/ntu-96-R94221012-1.pdf