3 citations · 5 across the 5 of their papers we have counts for
8 papers
Dragon curves in Littlewood roots
Marcus Michelen, Oren Yakir
A Littlewood polynomial is a polynomial whose coefficients lie in . While the majority of roots of a Littlewood polynomial of large degree are near the unit circle, nu…
The geometry of the giant component of random geometric graphs
Karoline Dubin, Christian Gorski, Marcus Michelen
Consider a random geometric graph whose vertex set consists of points chosen independently and uniformly from a Riemannian manifold , with edges joining pairs of…
Success probability for selectively neutral invading species in the line model with a random fitness landscape
Suzan Farhang-Sardroodi, Natalia L. Komarova, Marcus Michelen +1
We consider a spatial (line) model for invasion of a population by a single mutant with a stochastically selectively neutral fitness landscape, independent from the fitness landsca…
The frog model on non-amenable trees
Marcus Michelen, Josh Rosenberg
We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d. $\m…
The frog model on Galton-Watson trees
Marcus Michelen, Josh Rosenberg
We consider an interacting particle system on trees known as the frog model: initially, a single active particle begins at the root and i.i.d.~ many inactive par…
Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees
Marcus Michelen
We consider critical percolation on Galton-Watson trees and prove quenched analogues of classical theorems of critical branching processes. We show that the probability critical pe…
Quenched Survival of Bernoulli Percolation on Galton-Watson Trees
Marcus Michelen, Robin Pemantle, Josh Rosenberg
We explore the survival function for percolation on Galton-Watson trees. Letting represent the probability a tree survives Bernoulli percolation with parameter , we…
Invasion Percolation on Galton-Watson Trees
Marcus Michelen, Robin Pemantle, Josh Rosenberg
We consider invasion percolation on Galton-Watson trees. On almost every Galton-Watson tree, the invasion cluster almost surely contains only one infinite path. This means that for…