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math.PR2026
Universality of Large-Scale Geometry For Critical Random-Cluster Models
Ulrik Thinggaard Hansen, Ioan Manolescu
The understanding of the behaviour of critical lattice models in two dimensions has made immense progress in the past couple of decades, with conformal invariance as its conjecture…
math.PR2026
The End of the Double Random Current
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
The Ising correlation function can be expressed in terms of connectivity probabilities of a random graph known as the double random current. In 2016, Duminil-Copin asked whether th…
math.PR2026
The Supercritical Loop O(1) and Random Current models: Uniqueness and Mixing
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
Much recent rigorous study of the classical ferromagnetic Ising model has been powered by its graphical representations, such as the random current and loop O(1) model (high temper…