| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 伊凱馬 | zh_TW |
| DC.creator | Badr Saleh Badr Mohamed Elkamash | en_US |
| dc.date.accessioned | 2020-7-7T07:39:07Z | |
| dc.date.available | 2020-7-7T07:39:07Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=107221601 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 在本論文中，我們研究了Ising模型的Glauber動力學。基於[10]的專著，我們提供了馬爾可夫鏈混合時間一般理論的詳細介紹，尤其是收斂到平穩測度的速率。
然後，我們計算出Ising模型的兩個特殊（也許是最重要）案例的細節：直線和圓。
我們的貢獻是
（1） 我們針對這兩種特殊情況獲得了改進的估計；和
（2） 我們提供了許多細節和例子和圖片示例來說明該理論。
更詳細地，我們證明在高溫下快速混合。我們確定混合時間是log(n)和log(1/e)的多項式。或者，顯示tmix在log(n)也足以進行快速混合。我們證明了Glauber動力學的混合時間為在高溫下具有n個頂點的直線和圓上的（鐵磁）伊辛模型的上限為n log n/e。 | zh_TW |
| dc.description.abstract | In this thesis we study Glauber dynamics of one dimensional Ising models. We provide a detailed presentation of the general theory of the mixing times of Markov chains, especially the rate of convergence to stationary measures, based on the monograph of [10].
Then we work out the details of two special (and perhaps the most important) cases of Ising models: the line and the circle. Our contribution is that
(1) we obtain improved estimates for these two special cases; and
(2) we provide many examples with details and pictures to illustrate the theory.
In more details, we prove a fast mixing at high temperature. We establish that the mixing time is a polynomial in log(n) and log(1/e). Alternatively, we show that tmix is a polynomial in log(n). It is also enough for fast mixing. We show that the mixing time of Glauber dynamics for the (ferromagnetic) Ising model on a line and a circle with n vertices at high temperature has an upper bound of n log n/e. | en_US |
| DC.subject | 伊辛模型 | zh_TW |
| DC.subject | 格勞伯動力 | zh_TW |
| DC.subject | 混合時間 | zh_TW |
| DC.subject | 馬爾可夫鏈 | zh_TW |
| DC.subject | 路徑耦合 | zh_TW |
| DC.subject | Ising Model | en_US |
| DC.subject | Glauber Dynamics | en_US |
| DC.subject | Mixing Time | en_US |
| DC.subject | Markov Chains | en_US |
| DC.subject | Path Coupling | en_US |
| DC.title | Mixing Time for Ising Model (On Two Special Graphs: the Line and the Circle) | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |