A family of fractional diffusion equations derived from stochastic harmonic chains with long-range interactions
A family of fractional diffusion equations derived from stochastic harmonic chains with long-range interactions
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DOI：
10.1214/20-aihp1133
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发表时间：
2019-12
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影响因子：
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通讯作者：
H. Suda
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文献类型：
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作者：
H. Suda
本文考虑具有随机扰动和长程相互作用的一维无限长谐振子链，其衰减率为多项式。|X| ^{-\theta}，x \to \infty，\theta > 1$，其中x \in \mathbb{Z}$是相互作用范围。我们证明，如果$2 3$，那么指数是$\frac{3}{4}$。阈值为$ \theta = 3$，因为色散关系的导数在$\theta \le 3$时发散为$k \to 0$。
We consider one-dimensional infinite chains of harmonic oscillators with stochastic perturbations and long-range interactions which have polynomial decay rate $|x|^{-\theta}, x \to \infty, \theta > 1$, where $x \in \mathbb{Z}$ is the interaction range. We prove that if $2 3$, then the exponent is $\frac{3}{4}$. The threshold is $ \theta = 3$ because the derivative of the dispersion relation diverges as $k \to 0$ when $\theta \le 3$.