型仿射建筑物上杰出随机游走的锐估计 [公式省略]

Indagationes Mathematicae Pub Date : 2024-06-13 DOI:10.1016/j.indag.2024.06.002

Jean-Philippe Anker, Bruno Schapira, Bartosz Trojan

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引用次数: 0

摘要

我们研究的是类型为，的仿射建筑物上的一种杰出随机漫步，卡特赖特、萨洛夫-科斯特和沃斯已经考虑过这种漫步。在秩为 , 的情况下，它是简单随机游走，我们得到了其过渡密度的最优全局边界（相同的上界和下界，直到乘法常数）。在秩较高的情况下，我们在相当大的时空区域内获得了尖锐的均匀边界，这足以满足大多数应用的需要。

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Sharp estimates for distinguished random walks on affine buildings of type [formula omitted]

We study a distinguished random walk on affine buildings of type , which was already considered by Cartwright, Saloff-Coste and Woess. In rank , it is the simple random walk and we obtain optimal global bounds for its transition density (same upper and lower bound, up to multiplicative constants). In the higher rank case, we obtain sharp uniform bounds in fairly large space–time regions which are sufficient for most applications.

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Indagationes Mathematicae

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