Year: 2025
Type: article
Abstract: Consider a collaborative dynamic of k k independent random walks on a finite connected graph G G . We are interested in the size of the set of vertices visited by at least one walker and study how the number of walkers relates to the efficiency of covering the graph. To this end, we show that the expected size of the union of ranges of k k independent random walks with lifespans t 1 , t 2 , … , t k t_1,t_2,\ldots ,t_k , respectively, is greater than or equal to that of a single random walk with the lifespan equal to t 1 + t 2 + ⋯ + t k t_1+t_2+\cdots +t_k . We analyze other related graph exploration schemes and end with many open questions.
DOI: 10.1090/proc/17332
Authors: Partha S. Dey, Daesung Kim, Grigory Terlov
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414426885