3 papers
math.PR2026
Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation
Lucas D'Alimonte, Loïc Gassmann
We prove that, in the FK-percolation model, the probabilities of local events are uniformly analytic in the percolation parameter under suitable mixing assumptions on the measu…
math.PR2025
Comparison of arm exponents in planar FK-percolation
Loïc Gassmann, Ioan Manolescu
By the FKG inequality for FK-percolation, the probability of the alternating two-arm event is smaller than the product of the probabilities of having a primal arm and a dual arm, r…
math.PR2025
Ordering and Convergence of Large Degrees in Random Hyperbolic Graphs
Loïc Gassmann
We describe the asymptotic behaviour of large degrees in random hyperbolic graphs, for all values of the curvature parameter . We prove that, with high probability, the node d…