Lattice Random Walks in Focal Point Potentials
Published:Dec 30, 2025 17:10
•1 min read
•ArXiv
Analysis
This paper investigates the behavior of lattice random walkers in the presence of V-shaped and U-shaped potentials, bridging a gap in the study of discrete-space and time random walks under focal point potentials. It analyzes first-passage variables and the impact of resetting processes, providing insights into the interplay between random motion and deterministic forces.
Key Takeaways
- •Analyzes lattice random walks in V-shaped and U-shaped potentials.
- •Studies first-passage probability and its dependence on bias strength.
- •Investigates the effects of resetting processes on steady-state probability and first-passage dynamics.
- •Provides insights into the interplay between random motion and deterministic forces.
Reference
“The paper finds that the mean of the first-passage probability may display a minimum as a function of bias strength, depending on the location of the initial and target sites relative to the focal point.”