论文标题
相互作用粒子系统中的平均曲率运动
Motion by mean curvature in interacting particle systems
论文作者
论文摘要
在许多情况下，已证明重新固定的相互作用粒子系统会收敛到具有双重反应项的反应扩散方程（RDE）。这些RDE具有行驶波解决方案。当波的速度非零时，已使用块构造来证明非平稳分布的存在或不存在。在这里，我们遵循Etheridge，Freeman和Pennington的纸张中的方法，以表明，当RDE极限具有可行的反应项时，在各种各样的示例中，流动波的速度为0时，可以更快地运行时间，进一步恢复空间以通过平均曲率获得融合到运动。这打开了证明具有快速搅拌的有性繁殖模型的可能性不连续的相变，并且在Molofsky等人研究的非线性选民模型的第2区域中，有两个非平稳的固定分布。
There are a number of situations in which rescaled interacting particle systems have been shown to converge to a reaction diffusion equation (RDE) with a bistable reaction term. These RDEs have traveling wave solutions. When the speed of the wave is nonzero, block constructions have been used to prove the existence or nonexistence of nontrivial stationary distributions. Here, we follow the approach in a paper by Etheridge, Freeman, and Pennington to show that in a wide variety of examples when the RDE limit has a bistable reaction term and traveling waves have speed 0, one can run time faster and further rescale space to obtain convergence to motion by mean curvature. This opens up the possibility of proving that the sexual reproduction model with fast stirring has a discontinuous phase transition, and that in Region 2 of the phase diagram for the nonlinear voter model studied by Molofsky et al there were two nontrivial stationary distributions.
