Cutoff for rewiring dynamics on perfect matchings

Linking the mixing times of random walks on static and dynamic random graphs

“…Therefore, for q n ∼ Unif(I c,n ), any κ ∈ N and any sequence ( In [20] and [13, Section 5.2] it is noted that Schramm's coupling can be adapted to the setting of coagulation-fragmentation dynamics that keep the measure PoiDir(θ), θ ∈ (0, 1], invariant. An example is a dynamic graph model with all degrees equal to two and endowed with a rewiring dynamics, which corresponds to a coagulation-fragmentation dynamics with invariant measure PoiDir(1/2) (see [31]). Since ν θ (L ε ) > 0 for any θ, ε ∈ (0, 1) and ν θ = PoiDir(θ), the proof of Proposition C.10 can be adapted to the aforementioned situation.…”

“…Our techniques and results can be adapted to the setting where the underlying geometry is modelled by a graph process starting from the configuration where all the vertices have a self-loop, equipped with rewiring dynamics. This process has been previously studied in [31].…”