5 papers
Graph distance and effective resistance of the random walk trace in four and five dimensions
Arka Adhikari, Izumi Okada, Daisuke Shiraishi
In this paper, we prove that the fluctuations of the graph distance and the effective resistance on the trace of a random walk in four and five dimensions converge in distribution…
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…
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…
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…
Moderate Deviations for the Capacity of the Random Walk range in dimension four
Arka Adhikari, Izumi Okada
In this paper, we find a natural four dimensional analog of the moderate deviation results for the capacity of the random walk, which corresponds to Bass, Chen and Rosen \cite{BCR}…