论文标题
高斯上限，用于无限几何图的图表上的热核
Gaussian upper bounds for heat kernels on graphs with unbounded geometry
论文作者
论文摘要
我们证明，在具有无限几何形状的图表上，在图形上连续的时间热核具有大型高斯上限。我们的估计值适用于满足Sobolev不平等和体积增加一倍的大球中心。相对于具有有限距离球和有限跳跃大小的固有度量测量距离。高斯衰减是由戴维斯（Davies）的功能自然而清晰的davies衰减。此外，我们发现了一个新的多项式校正项，该校正项不会以零为零。尽管我们的主要重点是无限的拉普拉斯人，但即使对于标准化的拉普拉斯人来说，结果也是新的。在无界的顶点度或退化度量的情况下，估计值受反映几何学无限性的新误差术语的影响。
We prove large-time Gaussian upper bounds for continuous-time heat kernels of Laplacians on graphs with unbounded geometry. Our estimates hold for centers of large balls satisfying a Sobolev inequality and volume doubling. Distances are measured with respect to an intrinsic metric with finite distance balls and finite jump size. The Gaussian decay is given by Davies' function which is natural and sharp in the graph setting. Furthermore, we find a new polynomial correction term which does not blow up at zero. Although our main focus is unbounded Laplacians, the results are new even for the normalized Laplacian. In the case of unbounded vertex degree or degenerating measure, the estimates are affected by new error terms reflecting the unboundedness of the geometry.
