The first Dirichlet eigenvalue of birth-death process on tree

Wang Lingdi; Zhang Yuihui

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arXiv · 1304.5310

The first Dirichlet eigenvalue of birth-death process on tree

Wang Lingdi·Zhang Yuihui

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Abstract

This paper investigates the birth-death ("B-D" for short) process on tree with continuous time, emphasizing on estimating the principal eigenvalue (equivalently, the convergence rate) of the process with Dirichlet boundary at the unique root 0. Three kinds of variational formulas for the eigenvalue are presented. As an application, we obtain a criterion for positivity of the first eigenvalue for B-D processes on tree with one branch after some layer.

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Wang Lingdi, Zhang Yuihui. 2013-04-19. The first Dirichlet eigenvalue of birth-death process on tree. https://arxiv.org/abs/1304.5310

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