Geodesic Lévy flights and expected stopping time for random searches

• 成果类型: Article
• 署名作者: Chaubet, Yann; Bonthonneau, Yannick Guedes; Lefeuvre, Thibault; Tzou, Leo
• 署名单位: University of Cambridge; Universite Paris 13; Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Amsterdam
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01327-8
• 发表日期: 2025
• 页码: 235-285
• 关键词: narrow escape; asymptotic analysis; part ii

摘要

We give an analytic description for the infinitesimal generator constructed in Applebaum and Estrade (Ann Probab 28(1):166-184, 2000) for L & eacute;vy flights on a broad class of closed Riemannian manifolds including all negatively-curved manifolds, the flat torus and the sphere. Various properties of the associated semigroup and the asymptotics of the expected stopping time for L & eacute;vy flight based random searches for small targets, also known as the narrow capture problem, are then obtained using our newfound understanding of the infinitesimal generator. Our study also relates to the L & eacute;vy flight foraging hypothesis in the field of biology as we compute the expected time for finding a small target by using the L & eacute;vy flight random search. Compared to the random search time for Brownian motion on surfaces done in Nursultanov et al. (arXiv:2209.12425), our result suggests that L & eacute;vy flight may not always be the optimal strategy, consistent with the conclusion obtained in Palyulin et al. (Proc Natl Acad Sci 111(8):2931-2936, 2014) for the one dimensional case.