Probability
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Paper Directional zero–one laws beyond iid environments and iid ballisticity
On ℤd, d ≥ 3, directional escape has probability zero or one for iid strictly elliptic nearest-neighbor environments, and for stationary ergodic finite-range-dependent environments under uniform ellipticity. In iid…
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Paper Canonical O(3) continuum limit and exact O(4) mass asymptotics
Constructs the canonical continuum limit of the two-dimensional nearest-neighbor O(3) model: a non-Gaussian local relativistic theory with a unique vacuum and a positive mass gap. For the square-lattice O(4)…
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Paper Critical SK autocorrelation processes and dynamics across the temperature transition
For zero-field Gaussian SK heat-bath dynamics with rate-one updates per spin, proves worst-start cutoff on the \log n scale for fixed 0\le\beta\lt 1, mixing time n^{2/3+o(1)} at β = 1, and…
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Paper The exact factor-of-IID threshold for free Ising spins on trees
Determines when the free zero-field ferromagnetic Ising state on the infinite d-regular tree is a factor of independent vertex labels: exactly when \tanh\beta\le(d-1)^{-1/2}, including equality, for d ≥ 3 and β ≥ 0.…
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Paper Optimal logarithmic mixing of the Thorp shuffle
Proves that the Thorp shuffle randomizes N=2^d labeled cards in \Theta(\log N) physical shuffles, settling its optimal mixing order for power-of-two deck sizes. Convergence is in total variation from the worst…
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Paper The three-quarter exponent for honeycomb self-avoiding walk
Proves the diameter form of Nienhuis's predicted three-quarter exponent: a uniformly chosen n-step self-avoiding walk on the honeycomb lattice has diameter n^{3/4+o(1)}. Its local mass and covering numbers have…
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Paper Planar first-passage geometry and the absence of bigeodesics
Proves that planar first-passage percolation has no doubly infinite geodesic for iid nonnegative nonatomic edge weights when the minimum of four weights has finite second moment. For exponential weights, the limit shape…
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Paper Continuum phase transitions for radial pair potentials
Constructs stable distance-dependent pair interactions for three-dimensional classical particles with a first-order phase transition: the canonical free energy has a derivative jump at one inverse temperature throughout…
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Paper Critical percolation on every quasi-transitive graph
Resolves the Benjamini–Schramm criticality conjecture for bond percolation on every infinite connected locally finite quasi-transitive graph with pc\lt 1: at the critical probability, there is almost surely no…
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