Mixing Time
篇幅打算以例子為主。
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Local file Local file
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a similar way
the similar manner 這種有相似定義的名詞怎麼寫好呢？ - Similar的點怎麼描述
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Spectral Gap
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不知道章節引入點怎麼寫。 Dirichlet form 和 Spectral gap 不知道怎麼導入。
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要比較Note中的內容嗎？(關於 over complex number 和 over real numbers、Spectral gap 的另一種刻劃)
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Remark 3.1.3. Due to the linearity of inner products, if (3.1) holds for f = δx, g = δy wherex, y are two elements of S and δx stands for the Dirac delta function, then M is self-adjoint onℓ2(π). On the other hand, the explicit form of (3.1) shows that by considering K as an operatoron ℓ2(π), K is self-adjoint if π(x)K(x, y) = π(y)K(y, x).Remark 3.1.3 provides the connection between reversible transition matrices and self-adjointoperators.Theorem 3.1.4. Let K be an irreducible transition matrix having stationary distribution π. Kis reversible if and only if K is self-adjoint on ℓ2(π).
寫成 Thm. & Proof 會比較好嗎？
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Remark 3.1.2.
尚未完成。 為了 Theorem 3.1.5 中關於特徵值的論述。
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[ In this chapter, we consider irreducible transition matrix and the associated stationarydistribution. What should I type to reduce the repeated words?
想要預設第三章都是"irreducible transition matrix K with associated stationary distribution \pi"，該怎麼寫?
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