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This is a Quantitative Study study.

October 20, 2025Open Access

Large Deviations of First Passage Times of Branching Random Walks in Rᵈ: Asymptotics and Algorithms

Puntos clave

Large deviation probabilities of first passage times reveal critical insights in stochastic processes.
An asymptotically optimal polynomial-time algorithm computes lower large deviation probabilities effectively.
Numerical verification ensures the accuracy of the proposed algorithm for branching random walks.
Understanding microstructural features enhances the characterization of polymer strength and behavior.

Resumen

We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in Rᵈ where d 1. The FPT refers to the first time the BRW enters a ball of radius one with a distance x from the origin, conditioned upon the process's survival. Furthermore, we apply the spine decomposition technique to construct an asymptotically optimal polynomial-time algorithm for computing the lower large deviation probabilities of the FPT. The accuracy of our algorithm is also verified numerically. Our analysis not only provides a deeper theoretical understanding of these stochastic processes but also offers new insights into the microstructural features that are key to characterizing the strength of polymers.

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