Dr Tyler Helmuth's Outputs (2)

Directed Spatial Permutations on Asymmetric Tori (2024)
Journal Article
Hammond, A., & Helmuth, T. (in press). Directed Spatial Permutations on Asymmetric Tori. Annals of Probability,

We investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dirichlet distribution with parameter one. The asymmetry of the tori we c... Read More about Directed Spatial Permutations on Asymmetric Tori.

Percolation transition for random forests in d ⩾ 3 (2024)
Journal Article
Bauerschmidt, R., Crawford, N., & Helmuth, T. (2024). Percolation transition for random forests in d ⩾ 3. Inventiones Mathematicae, 237(2), 445-540. https://doi.org/10.1007/s00222-024-01263-3

The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor β>0 per edge. It arises as the q→0 limit of the q-state random cluster model with p=βq. We prove that in dimensions d⩾3... Read More about Percolation transition for random forests in d ⩾ 3.