A percolation formula.
Stationary measures for random walks in a random environment with random scenery.
Trees, not cubes: Hypercontractivity, cosiness, and noise stability.
On the cover time of planar graphs.
Percolation beyond , many questions and a few answers.
Recurrence of distributional limits of finite planar graphs.
SLE coordinate changes.
How to cage an egg.
Ends in uniform spanning forests.
One-arm exponent for critical 2D percolation.
Noise sensitivity of boolean functions and applications to percolation
Rigidity of circle domains whose boundary has ...-finite linear measure.
Markov chain intersections and the loop-erased walk
Values of brownian intersection exponents III : two-sided exponents
Poisson matching
Suppose that red and blue points occur as independent homogeneous Poisson processes in ℝ. We investigate translation-invariant schemes for perfectly matching the red points to the blue points. For any such scheme in dimensions =1, 2, the matching distance from a typical point to its partner must have infinite /2th moment, while in dimensions ≥3 there exist schemes where has finite exponential moments. The Gale–Shapley stable marriage is one natural matching scheme, obtained by iteratively matching...
Dynamical sensitivity of the infinite cluster in critical percolation
In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last decade. Here we focus on graphs which percolate at criticality, and investigate the dynamical sensitivity of the infinite cluster. We first give two examples of bounded degree graphs, one which percolates for all times at criticality and one which has exceptional...
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