Closed-form survival probabilities for biased random walks at arbitrary step number
Year: 2025
Type: article
Abstract: We present a closed-form expression for the survival probability of a biased random walker to first reach a target site on a one-dimensional lattice. The expression holds for any step number N and is computationally faster than non-closed-form results in the literature. Because our result is exact even in the intermediate step number range, it serves as a tool to study convergence to the large N limit. We also obtain a closed-form expression for the probability of last passage. In contrast to predictions of the large N approximation, the new expression reveals a critical value of the bias beyond which the tail of the last-passage probability decays monotonically.
Source: Physical Review Research
DOI: 10.1103/krxn-vqnt
Authors: Debendro Mookerjee, Sarah Kostinski
Institution: New York University
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: gold
Estimated APC paid: $2,625
OpenAlex ID: W4414799543