18 citations · 19 across the 2 of their papers we have counts for
4 papers · 1 filter
Heat-bath random walks with Markov bases
Caprice Stanley, Tobias Windisch
Graphs on lattice points are studied whose edges come from a finite set of allowed moves of arbitrary length. We show that the diameter of these graphs on fibers of a fixed integer…
The fiber dimension of a graph
Tobias Windisch
Graphs on integer points of polytopes whose edges come from a set of allowed differences are studied. It is shown that any simple graph can be embedded in that way. The minimal dim…
Rapid mixing and Markov bases
Tobias Windisch
The mixing behaviour of random walks on lattice points of polytopes using Markov bases is examined. It is shown that under a dilation of the underlying polytope, these random walks…
On the Connectivity of Fiber Graphs
Raymond Hemmecke, Tobias Windisch
We consider the connectivity of fiber graphs with respect to Gröbner basis and Graver basis moves. First, we present a sequence of fiber graphs using moves from a Gröbner basis and…