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arXiv · 1905.09504

Martin boundary of Brownian motion on Gromov hyperbolic metric graphs

Soonki Hong·Seonhee Lim
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Abstract

Let $\widetilde{X}$ be a locally finite complete Gromov hyperbolic metric graph with the geometric boundary consisting of infinitely many points. Suppose that there is a discrete subgroup of the isometry group $Iso(\widetilde{X})$ acting geometrically on $\widetilde{X}$. The $λ$-Martin boundary is the boundary of the image of an embedding from $\widetilde{X}$ to the space of $λ$-superharmonic functions. We show that the $λ$-Martin boundary coincides with the geometric boundary for any $λ\in [0, λ_0],$ in particular at the bottom of the spectrum $λ_0$.

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Soonki Hong, Seonhee Lim. 2020-12-15. Martin boundary of Brownian motion on Gromov hyperbolic metric graphs. https://arxiv.org/abs/1905.09504

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