3 papers
math.PR2026
Phase transition on the fluctuation of the structure of random walk ranges
Arka Adhikari, Izumi Okada
We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstra…
math.PR2026
Strassen's LIL and a Phase transition for the capacity of the random walk under diameter constraints
Arka Adhikari, Izumi Okada
We discuss the relationship between the capacity and the geometry for the range of the random walk for . In particular, we consider how efficiently the random walk moves or wh…
math.PR2025
Favorite sites for simple random walk in two and more dimensions
Chenxu Hao, Xinyi Li, Izumi Okada +1
On the trace of a discrete-time simple random walk on for , we consider the evolution of favorite sites, i.e., sites that achieve the maximal local time at…