92 citations · 395 across the 40 of their papers we have counts for
20 papers · 1 filter
Satisfiability and freezing in random integer programs
Dylan J. Altschuler, Ruben Ascoli, Will Perkins
We study a model of a random centrally symmetric polytope and ask about the existence of points in the polytope with non-zero, integer coordinates. Our main results are the locatio…
A simple proof of rapid mixing on random regular graphs beyond uniqueness
Andreas Göbel, Matthew Jenssen, Marcus Michelen +3
A recent breakthrough of Chen, Chen, Chen, Yin, and Zhang shows rapid mixing for Glauber dynamics for the hard-core model on random regular graphs beyond the tree uniqueness thresh…
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…
Strong spatial mixing for repulsive point processes
Marcus Michelen, Will Perkins
We prove that a Gibbs point process interacting via a finite-range, repulsive potential exhibits a strong spatial mixing property for activities , where is the…
Potential-weighted connective constants and uniqueness of Gibbs measures
Marcus Michelen, Will Perkins
We define a potential-weighted connective constant that measures the effective strength of a repulsive pair potential of a Gibbs point process modulated by the geometry of the unde…
Frozen -RSB structure of the symmetric Ising perceptron
Will Perkins, Changji Xu
We prove, under an assumption on the critical points of a real-valued function, that the symmetric Ising perceptron exhibits the `frozen 1-RSB' structure conjectured by Krauth and…
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…
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…
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…
Spin systems on Bethe lattices
Amin Coja-Oghlan, Will Perkins
In an extremely influential paper Mezard and Parisi put forward an analytic but non-rigorous approach called the cavity method for studying spin systems on the Bethe lattice, i.e.,…
Bethe states of random factor graphs
Amin Coja-Oghlan, Will Perkins
We verify a key component of the replica symmetry breaking hypothesis put forward in the physics literature [Mézard and Montanari 2009] on random factor graph models. For a broad c…
On the hard sphere model and sphere packings in high dimensions
Matthew Jenssen, Felix Joos, Will Perkins
We prove a lower bound on the entropy of sphere packings of of density . The entropy measures how plentiful such packings are, and our result is si…
Large Deviations for the Empirical Distribution in the General Branching Random Walk
Oren Louidor, Eliad Tsairi
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit…
Belief Propagation on replica symmetric random factor graph models
Amin Coja-Oghlan, Will Perkins
According to physics predictions, the free energy of random factor graph models that satisfy a certain "static replica symmetry" condition can be calculated via the Belief Propagat…
Limits of discrete distributions and Gibbs measures on random graphs
Amin Coja-Oghlan, Will Perkins, Kathrin Skubch
Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we constru…
Spectral Thresholds in the Bipartite Stochastic Block Model
Laura Florescu, Will Perkins
We consider a bipartite stochastic block model on vertex sets and , with planted partitions in each, and ask at what densities efficient algorithms can recover the parti…
Birthday Inequalities, Repulsion, and Hard Spheres
Will Perkins
We study a birthday inequality in random geometric graphs: the probability of the empty graph is upper bounded by the product of the probabilities that each edge is absent. We show…
On Sharp Thresholds in Random Geometric Graphs
Milan Bradonjić, Will Perkins
We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model o…
Large Deviations for the Empirical Distribution in the Branching Random Walk
Oren Louidor, Will Perkins
We consider the branching random walk on the real line where the underlying motion is of a simple random walk and branching is at least binary and at most decaying exponentially in…
The Forgetfulness of Balls and Bins
William Perkins
We find the asymptotic total variation distance between two distributions on configurations of m balls in n labeled bins: in the first, each ball is placed in a bin uniformly at ra…