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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.16795 |
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| _version_ | 1866911603834748928 |
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| author | Dai, Kang Wang, Jian |
| author_facet | Dai, Kang Wang, Jian |
| contents | We study long-time behaviors for branching-diffusion process corresponding to the drifted Schrödinger operator $\mathcal{L} = \frac{1}{2} Δ+ \langle \nabla V,\nabla \rangle - K$, where $K$ represents the reduction rate of a population dynamics and $\nabla V$ is a given drift term. In particular, we establish exponential convergence rates for the total mass of this process and characterize its quasi-stationary distribution. The proof is based on a novel transformation in spectral analysis, and heat kernel estimates for Schrödinger operators with unbounded potentials. The result is new even in the one-dimensional setting, which especially improves the recent work \cite{CMS}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16795 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-Time Behaviors of Branching-Diffusion Processes via Spectral Analysis Dai, Kang Wang, Jian Probability 60J85, 60J60, 47D08, 35K08 We study long-time behaviors for branching-diffusion process corresponding to the drifted Schrödinger operator $\mathcal{L} = \frac{1}{2} Δ+ \langle \nabla V,\nabla \rangle - K$, where $K$ represents the reduction rate of a population dynamics and $\nabla V$ is a given drift term. In particular, we establish exponential convergence rates for the total mass of this process and characterize its quasi-stationary distribution. The proof is based on a novel transformation in spectral analysis, and heat kernel estimates for Schrödinger operators with unbounded potentials. The result is new even in the one-dimensional setting, which especially improves the recent work \cite{CMS}. |
| title | Long-Time Behaviors of Branching-Diffusion Processes via Spectral Analysis |
| topic | Probability 60J85, 60J60, 47D08, 35K08 |
| url | https://arxiv.org/abs/2604.16795 |