56 citations · 120 across the 14 of their papers we have counts for
18 papers
Models of random spanning trees
Eric Babson, Moon Duchin, Annina Iseli +3
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest…
Redistricting for Proportionality
Moon Duchin, Gabe Schoenbach
American democracy is currently heavily reliant on plurality in single-member districts, or PSMD, as a system of election. But public perceptions of fairness are often keyed to par…
Spanning Trees and Redistricting: New Methods for Sampling and Validation
Sarah Cannon, Moon Duchin, Dana Randall +1
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Re…
Measuring Segregation via Analysis on Graphs
Moon Duchin, James M. Murphy, Thomas Weighill
In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus on a classical statistic from the geography and urban sociology literature known as…
A Computational Approach to Measuring Vote Elasticity and Competitiveness
Daryl DeFord, Moon Duchin, Justin Solomon
The recent wave of attention to partisan gerrymandering has come with a push to refine or replace the laws that govern political redistricting around the country. A common element…
Stars at infinity in Teichmüller space
Moon Duchin, Nathan Fisher
We investigate a metric structure on the Thurston boundary of Teichmüller space. To do this, we develop tools in sup metrics and apply Minsky's theorem.
Recombination: A family of Markov chains for redistricting
Daryl DeFord, Moon Duchin, Justin Solomon
Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, t…
Discrete geometry for electoral geography
Moon Duchin, Bridget Eileen Tenner
"Compactness," or the use of shape as a proxy for fairness, has been a long-running theme in the scrutiny of electoral districts; badly-shaped districts are often flagged as exampl…
Conjugation curvature for Cayley graphs
Assaf Bar-Natan, Moon Duchin, Robert Kropholler
We introduce a notion of Ricci curvature for Cayley graphs that can be thought of as "medium-scale" because it is neither infinitesimal nor asymptotic, but based on a chosen finite…
Random nilpotent groups I
Matthew Cordes, Moon Duchin, Yen Duong +2
We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the…
Rational growth in the Heisenberg group
Moon Duchin, Michael Shapiro
A group presentation is said to have rational growth if the generating series associated to its growth function represents a rational function. A long-standing open question asks w…
Equations in nilpotent groups
Moon Duchin, Hao Liang, Michael Shapiro
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commut…
Spheres in the curve complex
Spencer Dowdall, Moon Duchin, Howard Masur
In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Avera…
Filling loops at infinity in the mapping class group
Aaron Abrams, Noel Brady, Pallavi Dani +2
We study the Dehn function at infinity in the mapping class group, finding a polynomial upper bound of degree four. This is the same upper bound that holds for arbitrary right-angl…
Statistical hyperbolicity in Teichmüller space
Spencer Dowdall, Moon Duchin, Howard Masur
In this paper we explore the idea that Teichmüller space is hyperbolic "on average." Our approach focuses on studying the geometry of geodesics which spend a definite proportion of…
Pushing fillings in right-angled Artin groups
Aaron Abrams, Noel Brady, Pallavi Dani +2
We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use…
Length spectra and degeneration of flat metrics
Moon Duchin, Christopher J. Leininger, Kasra Rafi
In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of si…
Divergence of geodesics in Teichmuller space and the mapping class group
Moon Duchin, Kasra Rafi
We show that both Teichmuller space (with the Teichmuller metric) and the mapping class group (with a word metric) have geodesic divergence that is intermediate between the linear…