60 citations · 266 across the 44 of their papers we have counts for
4 papers · 1 filter
Local time on the exceptional set of dynamical percolation, and the Incipient Infinite Cluster
Alan Hammond, Gábor Pete, Oded Schramm
In dynamical critical site percolation on the triangular lattice or bond percolation on \Z^2, we define and study a local time measure on the exceptional times at which the origin…
Self-avoiding walk is sub-ballistic
Hugo Duminil-Copin, Alan Hammond
We prove that self-avoiding walk on Z^d is sub-ballistic in any dimension d at least two. That is, writing ||u|| for the Euclidean norm of u \in Z^d, and SAW_n for the uniform meas…
Sharp phase transition in the random stirring model on trees
Alan Hammond
We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists d_0…
Infinite cycles in the random stirring model on trees
Alan Hammond
We prove that, in the random stirring model of parameter T on an infinite rooted tree each of whose vertices has at least two offspring, infinite cycles exist almost surely, provid…