Ofer Zeitouni

Decay of Correlations for the Massless Hierarchical Liouville Model in Infinite Volume

Abstract Let $$A=(A_v)_{v\in \mathcal {T}}$$ A = ( A v ) v ∈ T be the balanced Gaussian Branching Random Walk on a d -ary tree $$\mathcal {T}$$ T and let $$M^A$$ M A be the multiplicative chaos with parameter $$\gamma \in (0, \sqrt{2\log d})$$ γ ∈ ( 0 , 2 log d ) constructed from...

Tightness of the maximum of Ginzburg–Landau fields

We consider the discrete Ginzburg–Landau field with potential satisfying a uniform convexity condition, in the critical dimension d=2, and prove that its maximum over boxes of sidelength N, centered by an explicit N-dependent centering, is tight.