5 citations · 6 across the 8 of their papers we have counts for
9 papers
Chase-escape with conversion as a multiple sclerosis lesion model
Emma Bailey, Erin Beckman, Saraí Hernández-Torres +8
We introduce conversion to the stochastic process known as chase-escape in an effort to model aspects of inflammatory damage from multiple sclerosis. We prove monotonicity results…
Inferring birth versus death dynamics for ecological interactions in stochastic heterogeneous populations
Erin Beckman, Heyrim Cho, Linh Huynh
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death proce…
The central limit theorem via doubling of variables
Louigi Addario-Berry, Gavin Barill, Erin Beckman +1
We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of s…
Symmetric cooperative motion in one dimension
Louigi Addario-Berry, Erin Beckman, Jessica Lin
We explore the relationship between recursive distributional equations and convergence results for finite difference schemes of parabolic partial differential equations (PDEs). We…
Asymmetric cooperative motion in one dimension
Louigi Addario-Berry, Erin Beckman, Jessica Lin
We prove distributional convergence for a family of random processes on , which we call asymmetric cooperative motions. The model generalizes the "totally asymmetric hi…
Chase-escape with death on trees
Erin Beckman, Keisha Cook, Nicole Eikmeier +2
Chase-escape is a competitive growth process in which red particles spread to adjacent uncolored sites, while blue particles overtake adjacent red particles. We introduce the varia…
The frog model on trees with drift
Erin Beckman, Natalie Frank, Yufeng Jiang +2
We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a -ary tree is recurrent. To do this, we introduce a subprocess that couples across…
Asymptotic behavior of the Brownian frog model
Erin Beckman, Emily Dinan, Rick Durrett +2
We introduce an extension of the frog model to Euclidean space and prove properties for the spread of active particles. Fix and place a particle at each point of a unit i…
Block size in Geometric(p)-biased permutations
Irina Cristali, Vinit Ranjan, Jake Steinberg +4
Fix a probability distribution on the positive integers. The first block in a -biased permutation can be visualized in terms of raindrop…