论文标题
高斯乘法混乱和应用的多重分析
Multifractal analysis of Gaussian multiplicative chaos and applications
论文作者
论文摘要
令$m_γ$为一个亚临界高斯乘法混乱度量，与在有界域上定义的一般对数相关的高斯字段相关联，该场$ d \ subset \ subset \ mathbb {r}^d $，$ d \ geq 1 $。我们通过表明$M_γ$几乎可以满足多重形式主义的肯定，即，即我们证明其奇异性频谱几乎肯定等于其$ l^q $ -spectrum的legendre-fenchel tronfrolut，我们发现其奇异性光谱的明确公式。然后，应用此结果，我们计算了多重随机步行和liouville Brownian运动的较低奇异性光谱。
Let $M_γ$ be a subcritical Gaussian multiplicative chaos measure associated with a general log-correlated Gaussian field defined on a bounded domain $D \subset \mathbb{R}^d$, $d \geq 1$. We find an explicit formula for its singularity spectrum by showing that $M_γ$ satisfies almost surely the multifractal formalism, i.e., we prove that its singularity spectrum is almost surely equal to the Legendre-Fenchel transform of its $L^q$-spectrum. Then, applying this result, we compute the lower singularity spectrum of the multifractal random walk and of the Liouville Brownian motion.
