厄任菲斯特甕的相變現象

Abstract

本論文主要為研究厄任菲斯特甕的相變現象，並證明了此現象存在性的等價條件。資料來源起於指導教授陳冠宇於2010年發表在Journal of Functional Analysis的文章The -cutoff for reversible Markov processes，而此文章已證明厄任菲斯特甕的相變存在性之充分條件。利用相變現象的存在性定義，我們先是證明了其不存在的充分條件。借此我們去證明原命題的逆否命題為真。

The main work of this thesis was giving a equivalent condition of the total variation cutoff for Ehrenfest chains. The source of the question came from my advisor Dr. Chen who had punished the paper, “The -cutoff for reversible Markov processes”, in Journal of Functional Analysis on 2010. And the paper had proven the sufficient condition of the total variation cutoff. We derived the sufficient condition for no cutoffs. Therefore, we proved the contrapositive true.