论文标题
混合型木村扩散的长时间渐近造型
Long time asymptotics of mixed-type Kimura diffusions
论文作者
论文摘要
本文涉及在域边界处具有退化系数的扩散的长期渐进率。使用混合线性和二次变性的退化扩散算子在分离拓扑绝缘子的边缘的不对称传输中发现了应用。在一个空间维度中，我们表征了此类操作员的所有可能不变度量，并且在所有情况下都显示了绿色的内核与此类不变措施的指数收敛。我们将结果推广到一类二维运算符，包括用于分析拓扑绝缘体的运算符。几个数值模拟说明了我们的理论发现。
This paper concerns the long-time asymptotics of diffusions with degenerate coefficients at the domain's boundary. Degenerate diffusion operators with mixed linear and quadratic degeneracies find applications in the analysis of asymmetric transport at edges separating topological insulators. In one space dimension, we characterize all possible invariant measures for such a class of operators and in all cases show exponential convergence of the Green's kernel to such invariant measures. We generalize the results to a class of two-dimensional operators including those used in the analysis of topological insulators. Several numerical simulations illustrate our theoretical findings.
