7 papers
A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting
Daryl R. DeFord, Gregory Herschlag, Jonathan C. Mattingly
We introduce the Cycle Walk, a new Markov chain Monte Carlo method for sampling distributions on balanced graph partitions, motivated by applications in political redistricting. Th…
A pathwise approach to the enhanced dissipation of passive scalars advected by shear flows
Victor Gardner, Kyle L. Liss, Jonathan C. Mattingly
We develop a framework for studying the enhanced dissipation of passive scalars advected by shear flows based on analyzing the particle trajectories of the stochastic differential…
Random Splitting of Point Vortex Flows
Andrea Agazzi, Francesco Grotto, Jonathan C. Mattingly
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the…
Central limit theorems for Fréchet means on stratified spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
Fréchet means of samples from a probability measure on any smoothly stratified metric space M with curvature bounded above are shown to satisfy a central limit theorem (CLT). T…
Geometry of measures on smoothly stratified metric spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
Any measure on a CAT(k) space M that is stratified as a finite union of manifolds and has local exponential maps near the Fréchet mean yields a continuous "tangential c…
Shadow geometry at singular points of CAT(k) spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of πor more with Z. Taking logarithm maps at points approaching p along…
A central limit theorem for random tangent fields on stratified spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
Variation of empirical Fréchet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows thes…