双曲图上的调和函数
Harmonic functions on hyperbolic graphs
摘要：
考虑双曲图上的容许随机游动。对于给定的调和函数，我们证明了非切有界性和非切收敛性的渐近性质是几乎处处等价的。证明的灵感来自F.收缩负曲率的黎曼流形和无限树情形下的Mouton。它涉及几何和概率方法。
英文摘要：
We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The proof is inspired by the works of F. Mouton in the cases of Riemannian manifolds of pinched negative curvature and infinite trees. It involves geometric and probabilitistic methods.
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