6 papers · 1 filter
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…
Capacity of the range of random walk: Moderate deviations in dimensions 4 and 5
Arka Adhikari, Jiyun Park
We prove a moderate deviation principle for the capacity of the range of random walk in . Depending on the scale of deviation, we get two different regimes. We observ…
Spectral measure for uniform -regular digraphs
Arka Adhikari, Amir Dembo
Consider the matrix chosen uniformly at random from the finite set of all -dimensional matrices of zero main-diagonal and binary entries, having each row and c…
The longest increasing subsequence of Brownian separable permutons
Arka Adhikari, Jacopo Borga, Thomas Budzinski +2
We establish a scaling limit result for the length of the longest increasing subsequence of a permutation of size sampled from the Brownian se…
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}…