無序混沌下SK模型上的中央極限定理

A central limit theorem for the overlaps in disorder chaos SK model

許景隆(Ching-Lung. Hsu)

指導教授 ： 許元春 ； 鄭志豪

國立清華大學/理學院/數學系/碩士(2017年)

摘要

這篇論文我們証明了在無序混沌下Sherrington-Kirkpatrick模型上的一個極限定理。這個定理主要是在描述來自兩個相關Gibbs測度的自旋結構重疊量的行為。我們將藉由Cavity方法來導出在給定一個無序態的時候，一群經過適當調整的重疊量在會在漸進行為上與高斯函數非常相像。

關鍵字

混沌 ； 重疊量 ； 中央極限定理

並列摘要

In this paper we consider a limiting theorem in disorder chaos Sherrington Kirkpatrick model. It is about the behavior of the overlaps between spin configurations sampled from two different correlated Gibbs measures. We use th cavity method to show that for a typical realization of the disorder, a family of the modified overlaps would behave asymptotically like an independent family of Gaussian random variables.

並列關鍵字

Chaos ； Overlap ； Central limit theorem

參考文獻

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