7 papers · 1 filter
Optimal Transport on Graphs and Stochastically Evolving Trees
Fan Chung, Sawyer Jack Robertson
We give an effective algorithm for determining the transportation distance between two given probability density functions defined on the vertices of a graph by analyzing…
Distance Exceptional Graphs and the Curvature Index
Sawyer Jack Robertson, Finn Southerland, Erlang Surya
A graph on vertices is said to be \emph{distance exceptional} if the equation admits no solution , where $D\in\mathbb{R…
Discrete Curvatures and Convex Polytopes
Jesús A. De Loera, Jillian Eddy, Sawyer Jack Robertson +1
We study Forman--Ricci and effective resistance curvatures on the skeleta of convex polytopes. Our guiding questions are: how frequently do polytopal graphs exhibit everywhere posi…
Stochastically Evolving Graphs via Edit Semigroups
Fan Chung, Sawyer Jack Robertson
We investigate a randomly evolving process of subgraphs in an underlying host graph using the spectral theory of semigroups related to the Tsetlin library and hyperplane arrangemen…
A Comparative Study of Curvature on Trees
Sawyer Jack Robertson
There are several interrelated notions of discrete curvature on graphs. Many approaches utilize the optimal transportation metric on its probability simplex or the distance matrix…
Harnack Inequality for Magnetic Graphs
Sawyer Jack Robertson
For magnetic graphs satisfying connection curvature dimension inequality , we prove a Harnack-type inequality for eigenfunctions of the graph magnetic Laplace operator i…
Kantorovich Duality and Optimal Transport Problems on Magnetic Graphs
Sawyer Jack Robertson
We consider Lipschitz- and Arens-Eells-type function spaces constructed for magnetic graphs, which are adapted to this setting from the area of optimal transport on discrete spaces…