论文标题
在$ \ mathbb {z}^2 $上进行曲率和大偏差的运动和大偏差
Motion by curvature and large deviations for an interface dynamics on $\mathbb{Z}^2$
论文作者
论文摘要
我们在$ \ mathbb {z}^2 $中研究Markov过程的大偏差，以模仿接口的运动。我们的动力学可以用参数$β$调节，该参数起着反向温度的作用，并以$β$ = $ = $ \ infty $重合具有GLAUBER动力学的零感染ising模型，其中曲线对应于另一个相位的滴剂的液滴边界。我们证明，轮廓通常会遵循曲率的运动，并影响参数$β$，并建立大的偏差界限。鉴定了模型的扩散系数和迁移率，并与文献中预测的相对应。
We study large deviations for a Markov process on curves in $\mathbb{Z}^2$ mimicking the motion of an interface. Our dynamics can be tuned with a parameter $β$, which plays the role of an inverse temperature, and coincides at $β$ = $\infty$ with the zero-temperature Ising model with Glauber dynamics, where curves correspond to the boundaries of droplets of one phase immersed in a sea of the other one. We prove that contours typically follow a motion by curvature with an influence of the parameter $β$, and establish large deviations bounds at all large enough $β$ < $\infty$. The diffusion coefficient and mobility of the model are identified and correspond to those predicted in the literature.
