46 citations · 133 across the 42 of their papers we have counts for
8 papers · 1 filter
Ricci curvature on birth-death processes
Bobo Hua, Florentin Münch
In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half…
Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds
Florentin Münch, Radoslaw K. Wojciechowski
Discrete time random walks on a finite set naturally translate via a one-to-one correspondence to discrete Laplace operators. Typically, Ollivier curvature has been investigated vi…
Magnetic sparseness and Schrödinger operators on graphs
Michel Bonnefont, Sylvain Golénia, Matthias Keller +2
We study magnetic Schrödinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnet…
State transfer in strongly regular graphs with an edge perturbation
Chris Godsil, Krystal Guo, Mark Kempton +1
Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state t…
Relationships between cycle spaces, gain graphs, graph coverings, fundamental groups, path homology, and graph curvature
Mark Kempton, Florentin Munch, Shing-Tung Yau
We prove a homology vanishing theorem for graphs with positive Bakry-Émery curvature, analogous to a classic result of Bochner on manifolds \cite{Bochner}. Specifically, we prove t…
Rigidity properties of the hypercube via Bakry-Emery curvature
Shiping Liu, Florentin Münch, Norbert Peyerimhoff
We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a…
Distance bounds for graphs with some negative Bakry-Émery curvature
Shiping Liu, Florentin Münch, Norbert Peyerimhoff +1
We prove distance bounds for graphs possessing positive Bakry-Émery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-po…
Ollivier-Ricci idleness functions of graphs
David Bourne, David Cushing, Shiping Liu +2
We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most linear pa…