38 citations · 136 across the 19 of their papers we have counts for
13 papers · 1 filter
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…
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…
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…
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…
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…
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…