38 citations · 136 across the 19 of their papers we have counts for
20 papers
Percolation on hypergraphs and the hard-core model
Tyler Helmuth, Will Perkins, Michail Sarantis
We prove tight bounds on the site percolation threshold for -uniform hypergraphs of maximum degree and for -uniform hypergraphs of maximum degree in which any pair of…
Directed Spatial Permutations on Asymmetric Tori
Alan Hammond, Tyler Helmuth
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--Dir…
Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature
Tyler Helmuth, Ryan L. Mann
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 perturbat…
Spin systems with hyperbolic symmetry: a survey
Roland Bauerschmidt, Tyler Helmuth
Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic mo…
Approximation algorithms for the random-field Ising model
Tyler Helmuth, Holden Lee, Will Perkins +2
Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and i…
Percolation transition for random forests in
Roland Bauerschmidt, Nicholas Crawford, Tyler Helmuth
The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor per edge. It arises as the limit o…
Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs
Tyler Helmuth, Matthew Jenssen, Will Perkins
For and 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 dete…
Efficient Algorithms for Approximating Quantum Partition Functions
Ryan L. Mann, Tyler Helmuth
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion o…
Loop-erased random walk as a spin system observable
Tyler Helmuth, Assaf Shapira
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…
Correlation decay for hard spheres via Markov chains
Tyler Helmuth, Will Perkins, Samantha Petti
We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions two and higher. As the dimension tends to infinity our i…
Random spanning forests and hyperbolic symmetry
Roland Bauerschmidt, Nicholas Crawford, Tyler Helmuth +1
We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter per edge. This is called the arboreal gas model, a…
Efficient sampling and counting algorithms for the Potts model on at all temperatures
Christian Borgs, Jennifer Chayes, Tyler Helmuth +2
For and all we give an efficient algorithm to approximately sample from the -state ferromagnetic Potts and random cluster models on finite tori $(\mat…
The continuous-time lace expansion
David C. Brydges, Tyler Helmuth, Mark Holmes
We derive a continuous-time lace expansion for a broad class of self-interacting continuous-time random walks. Our expansion applies when the self-interaction is a sufficiently nic…
The geometry of random walk isomorphism theorems
Roland Bauerschmidt, Tyler Helmuth, Andrew Swan
The classical random walk isomorphism theorems relate the local times of a continuous-time random walk to the square of a Gaussian free field. A Gaussian free field is a spin syste…
Algorithmic Pirogov-Sinai theory
Tyler Helmuth, Will Perkins, Guus Regts
We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of…
Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process
Roland Bauerschmidt, Tyler Helmuth, Andrew Swan
We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The…
Self-attracting self-avoiding walk
Alan Hammond, Tyler Helmuth
This article is concerned with self-avoiding walks (SAW) on that are subject to a self-attraction. The attraction, which rewards instances of adjacent parallel edg…
Dimensional reduction for generalized continuum polymers
Tyler Helmuth
The Brydges-Imbrie dimensional reduction formula relates the pressure of a -dimensional gas of hard spheres to a model of -dimensional branched polymers. Brydges and Imbr…
Loop-weighted Walk
Tyler Helmuth
Loop-weighted walk with parameter is a non-Markovian model of random walks that is related to the loop model of statistical mechanics. A walk receives weight $λ^{k…
Ising Model Observables and Non-Backtracking Walks
Tyler Helmuth
This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph and the set of non-backtracking walks on . The…