Dynamic large deviations: nucleation and growth in phase transitions and avalanches in random hamiltonian systems

随机扰动允许从确定性演化的大偏差，例如从（确定性）稳定状态的逃逸。我们调查动态大偏差在两个不同的上下文中：多相材料中的相边界的演变的介观模型，和过阻尼Langevin动力学与“摆动”的潜在的可能modelforavalches.The第一个问题的重点是良好的速率泛函的存在性和定性性质和宏观演化的约束下的极小化的特征。一个特别的例子是固定状态之间的切换（隧道）的确定性evolution.The第二个问题的目的是确定一个简化的随机哈密顿系统的一个适当的大偏差缩放的潜在的，具有高度振荡（“摆动”）的一部分的随机动态。主要的问题是，这是否可以作为雪崩的模型。

Stochastic perturbations allow for large deviations from the deterministic evolutions, as for example the escape from (deterministically) stationary states. We investigate dynamic large deviations in two different contexts: mesoscale models for the evolution of phase boundaries in multi-phase materials, and overdamped Langevin dynamics with a 'wiggly' potential as a possible model for avalanches.The focus of the first problem is on the existence and qualitative properties of good rate functionals and the characterisation of minimisers under constraints on the macroscopic evolution. A particular example is the switching (tunneling) between stationary states of the deterministic evolution.The aim of the second problem is to identify a stochastic dynamic in a suitable large deviations scaling of a simplified random Hamiltonian system with a potential that has a highly oscillating ('wiggly') part. The main question is whether this can serve as a model for avalanches.