Percolation since Saint-Flour

Abstract

This is a short survey of work on percolation and first-passage percolation since the publication (in 1996 and 1984, respectively) of the two authors' Saint-Flour notes on these topics.

References in corpus (16)

• Recent progress on the Random Conductance Model
• The critical probability for random Voronoi percolation in the plane is 1/2
• The Alexander-Orbach conjecture holds in high dimensions
• Lectures on Self-Avoiding Walks
• The Scaling Limit Geometry of Near-Critical 2D Percolation
• Conformal invariance of lattice models
• Inhomogeneous bond percolation on square, triangular and hexagonal lattices
• The near-critical planar FK-Ising model
• First passage percolation and competition models
• Conformal Invariance of Spin Correlations in the Planar Ising Model
• Schramm's proof of Watts' formula
• Lectures on noise sensitivity and percolation
• Upper large deviations for the maximal flow in first passage percolation
• Properties of the limit shape for some last passage growth models in random environments
• Clairvoyant embedding in one dimension
• Planar percolation with a glimpse of Schramm-Loewner Evolution

Cited by in corpus (11)

• Sublinear variance in first-passage percolation for general distributions
• Subdiffusive concentration in first-passage percolation
• Liouville first passage percolation: the weight exponent is strictly less than 1 at high temperatures
• Non-universality for first passage percolation on the exponential of log-correlated Gaussian fields
• Asymptotics for $2D$ Critical First Passage Percolation
• A proof of the bunkbed conjecture for the complete graph at $p=\frac{1}{2}$
• Limit theorems for critical first-passage percolation on the triangular lattice
• Busemann functions and infinite geodesics in two-dimensional first-passage percolation
• Asymptotic behavior of the Eden model with positively homogeneous edge weights
• Law of large numbers for critical first-passage percolation on the triangular lattice
• Multi-arm incipient infinite clusters in 2D: scaling limits and winding numbers