Towards Rigorous Results for Glassy Dynamics

从随机性和几何之间的相互作用中出现的新现象在许多物理实例中都是一个重要的机制，例如结构形成、渗透、相变，以及在流体、玻璃和堵塞填料中看到的相关空间随机性。然而，严谨的结果往往很少在感兴趣的物理模型中，而许多严谨的数学结果往往很少在物理环境中得到重视。从物理学的角度来看，简单的精确可解模型使人们能够非常清楚地阐明现象的潜在机制。

The emergence of new phenomena from the interplay between randomness and geometry is a vital mechanism in many instances in physics, such as structure formation, percolation, phase transitions, as well as the correlated spatial randomness seen in fluids, glasses and jammed packings. However, rigorous results are often rare in models of interest in physics, while many rigorous results from mathematics are often little appreciated in the physics contexts. From a physics perspective, simple exactly solvable models allow one to elucidate the underlying mechanisms of phenomena with great clarity.