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· 1 citation
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
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
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