Noise sensitivity of crossings for high temperature Ising model

2025/05/16 by Tassion, Vincent, Vanneuville, Hugo · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2505.11457

Abstract

Consider the event that there is a + crossing from left to right in a box for the Ising model on the triangular lattice. We show that this event is noise sensitive under Glauber dynamics t ↦ σ_t in the subcritical regime β<β_c. We rely on the non-spectral approach from our previous work [TV23]. An important aspect in this more general setup is the study of the pair (σ₀,σ_t) and in particular the establishment of properties such as finite-energy and spatial mixing.

Citations

• Strict inequalities for arm exponents in planar percolation
• Sparse reconstruction in spin systems II: Ising and other factor of IID measures
• Near critical scaling relations for planar Bernoulli percolation without\n differential inequalities
• Planar random-cluster model: scaling relations
• Noise sensitivity of percolation via differential inequalities
• Crossing probabilities for planar percolation
• The annealed spectral sample of Voronoi percolation
• Bargmann-Fock percolation is noise sensitive
• Liouville dynamical percolation
• Renormalization of crossing probabilities in the planar random-cluster model
• Exceptional times for percolation under exclusion dynamics
• Alternating Arm Exponents for the Critical Planar Ising Model
• Quenched Voronoi percolation
• The scaling limits of near-critical and dynamical percolation
• Lectures on noise sensitivity and percolation
• Exclusion Sensitivity of Boolean Functions
• Near-critical percolation in two dimensions
• Quantitative noise sensitivity and exceptional times for percolation

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