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Dr Tyler Helmuth's Outputs (13)

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.

Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature (2023)
Journal Article
Helmuth, T., & Mann, R. L. (2023). Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature. Quantum, 7, 1155. https://doi.org/10.22331/q-2023-10-25-1155

We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on combining th... Read More about Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature.

Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs (2023)
Journal Article
Helmuth, T., Jenssen, M., & Perkins, W. (2023). Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 59(2), 817-848. https://doi.org/10.1214/22-aihp1263

For ∆ ≥ 5 and q large as a function of ∆, we give a detailed picture of the phase transition of the random cluster model on random ∆-regular graphs. In particular, we determine the limiting distribution of the weights of the ordered and disordered ph... Read More about Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs.

Efficient sampling and counting algorithms for the Potts model on Zd at all temperatures (2022)
Journal Article
Borgs, C., Chayes, J., Helmuth, T., Perkins, W., & Tetali, P. (2023). Efficient sampling and counting algorithms for the Potts model on Zd at all temperatures. Random Structures and Algorithms, 63(1), 130-170. https://doi.org/10.1002/rsa.21131

The damselflies Hetaerininae, a subfamily of Calopterygidae, comprise four genera distributed from North to South America: Hetaerina, Mnesarete, Ormenophlebia and Bryoplathanon. While several studies have focused on the intriguing behavioral and morp... Read More about Efficient sampling and counting algorithms for the Potts model on Zd at all temperatures.

Spin systems with hyperbolic symmetry: a survey (2022)
Presentation / Conference Contribution
Bauerschmidt, R., & Helmuth, T. (2022, July). Spin systems with hyperbolic symmetry: a survey. Paper presented at International Congress of Mathematicians, 2022

Correlation decay for hard spheres via Markov chains (2022)
Journal Article
Helmuth, T., Perkins, W., & Petti, T. (2022). Correlation decay for hard spheres via Markov chains. Annals of Applied Probability, 32(3), 2063-2082. https://doi.org/10.1214/21-aap1728

We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions three and higher. As the dimension tends to infinity, our improvements are by factors of 2 and 1.7, respectively. We make thes... Read More about Correlation decay for hard spheres via Markov chains.

The geometry of random walk isomorphism theorems (2021)
Journal Article
Bauerschmidt, R., Helmuth, T., & Swan, A. (2021). The geometry of random walk isomorphism theorems. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 57(1), 408-454. https://doi.org/10.1214/20-aihp1083

The classical random walk isomorphism theorems relate the local times of a continuoustime random walk to the square of a Gaussian free field. A Gaussian free field is a spin system that takes values in Euclidean space, and this article generalises th... Read More about The geometry of random walk isomorphism theorems.

Random spanning forests and hyperbolic symmetry (2020)
Journal Article
Bauerschmidt, R., Crawford, N., Helmuth, T., & Swan, A. (2020). Random spanning forests and hyperbolic symmetry. Communications in Mathematical Physics, 381, 1223-1261. https://doi.org/10.1007/s00220-020-03921-y

We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter β>0 per edge. This is called the arboreal gas model, and the special case when β=1 is the uniform forest model. The arboreal g... Read More about Random spanning forests and hyperbolic symmetry.

Loop-Erased Random Walk as a Spin System Observable (2020)
Journal Article
Helmuth, T., & Shapira, A. (2020). Loop-Erased Random Walk as a Spin System Observable. Journal of Statistical Physics, 181(4), 1306-1322. https://doi.org/10.1007/s10955-020-02628-7

The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i.e., the probability a loop-erased random walk passes through a given... Read More about Loop-Erased Random Walk as a Spin System Observable.