2020/09/08 by Kui Liu, Liu, Kui, Xianchang Meng +1
Mathematics · Physics and Astronomy · #11H06 #11N37 #60G50 #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2009.03609
openalex publication_date 2020/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random walker visible from multiple watchpoints; (3) simultaneous visibility of multiple random walkers. Moreover, we found new phenomenon in the case of multiple random walkers: for visibility along a large class of curves and for any number of random walkers, the proportion of steps at which all random walkers are visible simultaneously is almost surely larger than a positive constant.