7 citations · 9 across the 6 of their papers we have counts for
8 papers
Sublinear variance in Euclidean first-passage percolation
Megan Bernstein, Michael Damron, Torin Greenwood
The Euclidean first-passage percolation model of Howard and Newman is a rotationally invariant percolation model built on a Poisson point process. It is known that the passage time…
Algebraic Voting Theory & Representations of
Hélène Barcelo, Megan Bernstein, Sarah Bockting-Conrad +3
We consider the problem of selecting an -member committee made up of one of candidates from each of distinct departments. Using an algebraic approach, we analyze positio…
Cutoff for biased transpositions
Megan Bernstein, Nayantara Bhatnagar, Igor Pak
In this paper we study the mixing time of a biased transpositions shuffle on a set of cards with cards of two types. For a parameter , one type of card is chos…
Analyzing Boltzmann Samplers for Bose-Einstein Condensates with Dirichlet Generating Functions
Megan Bernstein, Matthew Fahrbach, Dana Randall
Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1)…
On sampling graphical Markov models
Megan Bernstein, Prasad Tetali
We consider sampling and enumeration problems for Markov equivalence classes. We create and analyze a Markov chain for uniform random sampling on the DAGs inside a Markov equivalen…
Cutoff for random to random card shuffle
Megan Bernstein, Evita Nestoridi
In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Su…