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arXiv · 2405.20571

On the principal eigenvalue for compound Poisson processes

Daesung Kim·Hyunchul Park
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Abstract

We investigate the explicit expression for the principal eigenvalue $\lambda_{1}^{X}(D)$ for a large class of compound Poisson processes $X$ on a bounded open set $D$ by examining its spectral heat content. When the jump density of the compound Poisson process is radially symmetric and strictly decreasing, we demonstrate that balls are the unique minimizers for $\lambda_{1}^{X}(D)$ among all sets with equal Lebesgue measure. Furthermore, we show that this uniqueness fails if the jump density is not strictly decreasing.

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Daesung Kim, Hyunchul Park. 2024-05-31. On the principal eigenvalue for compound Poisson processes. https://arxiv.org/abs/2405.20571

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