92 citations · 395 across the 40 of their papers we have counts for
14 papers · 1 filter
On the zeroes of hypergraph independence polynomials
David Galvin, Gwen McKinley, Will Perkins +2
We study the locations of complex zeroes of independence polynomials of bounded degree hypergraphs. For graphs, this is a long-studied subject with applications to statistical phys…
Independent sets of a given size and structure in the hypercube
Matthew Jenssen, Will Perkins, Aditya Potukuchi
We determine the asymptotics of the number of independent sets of size in the discrete hypercube for any fixed as $d \to \…
Maximum entropy and integer partitions
Gweneth McKinley, Marcus Michelen, Will Perkins
We derive asymptotic formulas for the number of integer partitions with given sums of th powers of the parts for belonging to a finite, non-empty set .…
A proof of the Upper Matching Conjecture for large graphs
Ewan Davies, Matthew Jenssen, Will Perkins
We prove that the `Upper Matching Conjecture' of Friedland, Krop, and Markström and the analogous conjecture of Kahn for independent sets in regular graphs hold for all large enoug…
On the Number of Independent Sets in Uniform, Regular, Linear Hypergraphs
Emma Cohen, Will Perkins, Michail Sarantis +1
We study the problems of bounding the number weak and strong independent sets in -uniform, -regular, -vertex linear hypergraphs with no cross-edges. In the case of weak in…
Independent sets in the hypercube revisited
Matthew Jenssen, Will Perkins
We revisit Sapozhenko's classic proof on the asymptotics of the number of independent sets in the discrete hypercube and Galvin's follow-up work on weighted independent…
Tight bounds on the coefficients of partition functions via stability
Ewan Davies, Matthew Jenssen, Will Perkins +1
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. Fo…
Extremes of the internal energy of the Potts model on cubic graphs
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs…
The Widom-Rowlinson model, the hard-core model and the extremality of the complete graph
Emma Cohen, Péter Csikvári, Will Perkins +1
Let be the path on vertices with a loop at each vertex. D. Galvin conjectured, and E. Cohen, W. Perkins and P. Tetali proved that for any -regular simple g…
On the average size of independent sets in triangle-free graphs
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on vertices with maximum degree , showing that an independent s…
On the Widom-Rowlinson Occupancy Fraction in Regular Graphs
Emma Cohen, Will Perkins, Prasad Tetali
We consider the Widom-Rowlinson model of two types of interacting particles on d-regular graphs. We prove a tight upper bound on the occupancy fraction, the expected fraction of ve…
Independent Sets, Matchings, and Occupancy Fractions
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove tight upper bounds on the logarithmic derivative of the independence and matching polynomials of d-regular graphs. For independent sets, this theorem is a strengthening of…
Random k-SAT and the Power of Two Choices
Will Perkins
We study an Achlioptas-process version of the random k-SAT process: a bounded number of k-clauses are drawn uniformly at random at each step, and exactly one added to the growing f…
The Bohman-Frieze Process Near Criticality
Mihyun Kang, Will Perkins, Joel Spencer
The Erdős-Rényi process begins with an empty graph on n vertices and edges are added randomly one at a time to a graph. A classical result of Erdős and Rényi states that the Erdős-…