有限维欧氏空间中Parisi景观的显式构造
On an explicit construction of Parisi landscapes in finite dimensional Euclidean spaces
摘要：
我们构建了一个N维高斯景观多尺度，平移不变，对数相关性和调查的统计力学的单个粒子在这种环境中。在高维N>>1的极限下，热力学极限下系统的自由能与德里达广义随机能量模型的最一般版本一致。低温行为基本上取决于景观构造中所涉及的长度尺度谱。我们认为，我们的建设实际上是有效的，在任何有限的空间维度，从N=1。
英文摘要：
We construct a N-dimensional Gaussian landscape with multiscale, translation invariant, logarithmic correlations and investigate the statistical mechanics of a single particle in this environment. In the limit of high dimension N>>1 the free energy of the system in the thermodynamic limit coincides with the most general version of Derrida's Generalized Random Energy Model. The low-temperature behaviour depends essentially on the spectrum of length scales involved in the construction of the landscape. We argue that our construction is in fact valid in any finite spatial dimensions, starting from N=1.
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