8 citations · 16 across the 6 of their papers we have counts for
7 papers
Proof of the Diaconis--Freedman Conjecture on partially-exchangeable processes
Noah Halberstam, Tom Hutchcroft
We prove a conjecture of Diaconis and Freedman (Ann. Probab. 1980) characterising the extreme points of the set of partially-exchangeable processes on a countable set. More concret…
Uniqueness of the infinite tree in low-dimensional random forests
Noah Halberstam, Tom Hutchcroft
The arboreal gas is the random (unrooted) spanning forest of a graph in which each forest is sampled with probability proportional to for some , whic…
Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree
Noah Halberstam, Tom Hutchcroft
We compute the precise logarithmic corrections to Alexander-Orbach behaviour for various quantities describing the geometric and spectral properties of the four-dimensional uniform…
Most transient random walks have infinitely many cut times
Noah Halberstam, Tom Hutchcroft
We prove that if is a random walk on a transient graph such that the Green's function decays at least polynomially along the random walk, then h…
What are the limits of universality?
Noah Halberstam, Tom Hutchcroft
It is a central prediction of renormalisation group theory that the critical behaviours of many statistical mechanics models on Euclidean lattices depend only on the dimension and…
Lower Gaussian heat kernel bounds for the Random Conductance Model in a degenerate ergodic environment
Sebastian Andres, Noah Halberstam
We study the random conductance model on with ergodic, unbounded conductances. We prove a Gaussian lower bound on the heat kernel given a polynomial moment condition…
Collisions of Random Walks in Dynamic Random Environments
Noah Halberstam, Tom Hutchcroft
We study dynamic random conductance models on in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove un…