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math.PR2026
On the rigidity of sloped height functions in and non-crossing surfaces
Arka Adhikari, Reza Gheissari, Ron Peled
We consider integer-valued height functions, with general convex interactions, placed on a slope. Sheffield (2003) conjectured that for all slopes, such height functions…
math.PR2026
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…
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…