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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
On the critical fugacity of the hard-core model on regular bipartite graphs
Daniel Hadas, Ron Peled
We establish long-range order for the hard-core model on a finite, regular bipartite graph above a threshold fugacity given in terms of expansion parameters of the graph. The resul…
math.PR2025
Minimal surfaces in strongly correlated random environments
Barbara Dembin, Dor Elboim, Ron Peled
A minimal surface in a random environment (MSRE) is a -dimensional surface in -dimensional space which minimizes the sum of its elastic energy and its environment potenti…