17 citations · 67 across the 24 of their papers we have counts for
28 papers · 1 filter
Disks, Surfaces, and Entanglement Percolation
Paul Duncan, Benjamin Schweinhart, David Sivakoff
We study the probability that a loop is null-homotopic -- that is, bounded by the continuous image of a disk -- in plaquette percolation on Locally, the event that…
The effects of individual versus community-influenced isolation on SIS epidemic persistence on finite random graphs
Shirshendu Chatterjee, David Sivakoff, Matthew Wascher
The contact process, or the SIS epidemic model, is a continuous-time Markov process used to model the spread of a recurring infection on a graph. Each vertex is either healthy or i…
On the Continuity of Enhancement Percolation
Paul Duncan, Benjamin Schweinhart, David Sivakoff
We study bond percolation in with an unbounded family of enhancements that enable additional bonds to act as open. A natural question is whether percolation occurs i…
Two-stage Bootstrap Percolation
Zihao Fang, Janko Gravner, David Sivakoff
We introduce and study two variants of two-stage growth dynamics in with state space . In each variant, vertices in state can be change…
Polluted Modified Bootstrap Percolation
Janko Gravner, Alexander Holroyd, Sangchul Lee +1
In the polluted modified bootstrap percolation model, sites in the square lattice are independently initially occupied with probability or closed with probability . A site b…
Competing deterministic growth models in two dimensions
Janko Gravner, David Sivakoff
We consider three-state cellular automata in two dimensions in which two colored states, blue and red, compete for control of the empty background, starting from low initial densit…
Diffusion-limited annihilating-coalescing systems
Sungwon Ahn, Matthew Junge, Hanbaek Lyu +3
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both…
Two-dimensional supercritical growth dynamics with one-dimensional nucleation
Daniel Blanquicett, Janko Gravner, David Sivakoff +1
We introduce a class of cellular automata growth models on the two-dimensional integer lattice with finite cross neighborhoods. These dynamics are determined by a Young diagram $\m…
Cyclic Cellular Automata and Greenberg-Hastings Models on Regular Trees
Jason Bello, David Sivakoff
We study the cyclic cellular automaton (CCA) and the Greenberg-Hastings model (GHM) with colors and contact threshold on the infinite -regular tree, .…
Stretched exponential decay for subcritical parking times on
Michael Damron, Hanbaek Lyu, David Sivakoff
In the parking model on , each vertex is initially occupied by a car (with probability ) or by a vacant parking spot (with probability ). Cars perform indepen…
Particle density in diffusion-limited annihilating systems
Tobias Johnson, Matthew Junge, Hanbaek Lyu +1
Place an -particle at each site of a graph independently with probability and otherwise place a -particle. - and -particles perform independent continuous time rand…
Sampling random graph homomorphisms and applications to network data analysis
Hanbaek Lyu, Facundo Memoli, David Sivakoff
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large netwo…
Two-type annihilating systems on the complete and star graph
Irina Cristali, Yufeng Jiang, Matthew Junge +3
Red and blue particles are placed in equal proportion through-out either the complete or star graph and iteratively sampled to take simple random walk steps. Mutual annihilation oc…
The effect of avoiding known infected neighbors on the persistence of a recurring infection process
Shirshendu Chatterjee, David Sivakoff, Matthew Wascher
We study a generalization of the classical contact process (SIS epidemic model) in a directed graph . Our model is a continuous-time interacting particle system in which at ever…
Bootstrap percolation on the product of the two-dimensional lattice with a Hamming square
Janko Gravner, David Sivakoff
Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least occupied neighbors. The initiall…
Parking on transitive unimodular graphs
Michael Damron, Janko Gravner, Matthew Junge +2
Place a car independently with probability at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent r…
Coarsening model on with biased zero-energy flips and an exponential large deviation bound for ASEP
Michael Damron, Leonid Petrov, David Sivakoff
We study the coarsening model (zero-temperature Ising Glauber dynamics) on (for ) with an asymmetric tie-breaking rule. This is a Markov process on the sta…
Polluted Bootstrap Percolation in Three Dimensions
Janko Gravner, Alexander E. Holroyd, David Sivakoff
In the polluted bootstrap percolation model, vertices of the cubic lattice are independently declared initially occupied with probability or closed with probabil…
Persistence of sums of correlated increments and clustering in cellular automata
Hanbaek Lyu, David Sivakoff
We consider sums of increments given by a functional of a stationary Markov chain. Letting be the first return time of the partial sums process to , under general…
Phase transition in one-dimensional excitable media with variable interaction range
Ander Aguirre, Hanbaek Lyu, David Sivakoff
We investigate two discrete models of excitable media on a one-dimensional integer lattice : the -color Cyclic Cellular Automaton (CCA) and the -color Firefly Cel…
Limiting behavior of 3-color excitable media on arbitrary graphs
Janko Gravner, Hanbaek Lyu, David Sivakoff
Fix a simple graph and choose a random initial 3-coloring of vertices drawn from a uniform product measure. The 3-color cycle cellular automaton is a process in which at…
Bootstrap percolation on products of cycles and complete graphs
Janko Gravner, David Sivakoff
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least occupied neighbors. The initially occupied set is random, given…
Deterministic walk in an excited random environment
Ivan Matic, David Sivakoff
Deterministic walk in an excited random environment is a non-Markov integer-valued process , whose jump at time depends on the number of visits to the sit…
Nucleation scaling in jigsaw percolation
Janko Gravner, David Sivakoff
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on…