Author

A. Adhikari

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Preprint Sep 2026

On the rigidity of sloped height functions in $d\ge 3$ and non-crossing surfaces

We consider integer-valued $\nabla\phi$ height functions, with general convex interactions, placed on a slope. Sheffield (2003) conjectured that for all slopes, such height functions are localized in dimensions $d\ge3$, in the sense of having tight fluctuations in finite volume, and admitting infinite-volume limits. We...

A. Adhikari, Reza Gheissari, Ron Peled · 0 citations

Preprint Aug 2026

Graph distance and effective resistance of the random walk trace in four and five dimensions

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 to a stable law. In previous work, the first and second authors proved that the corresponding fluctuations converge to a Gaussian distributi...

A. Adhikari, Izumi Okada, D. Shiraishi · 0 citations