5 citations · 9 across the 8 of their papers we have counts for
8 papers · 1 filter
A subperiodic tree whose intermediate branching number is strictly less than the lower intermediate growth rate
Pengfei Tang
We construct an example of a subperiodic tree whose intermediate branching number is strictly less than the lower intermediate growth rate. This answers a question of Amir and Yang…
The wired minimal spanning forest on the Poisson-weighted infinite tree
Asaf Nachmias, Pengfei Tang
We study the spectral and diffusive properties of the wired minimal spanning forest (WMSF) on the Poisson-weighted infinite tree (PWIT). Let be the tree containing the root in…
Return probabilities on nonunimodular transitive graphs
Pengfei Tang
Consider simple random walk on a transitive graph with spectral radius . Let be the -step return probability and be the first…
A note on some critical thresholds of Bernoulli percolation
Pengfei Tang
Consider Bernoulli bond percolation on a locally finite, connected graph and let be the threshold corresponding to a "first-moment method" lower bound. Kahn…
Weights of uniform spanning forests on nonunimodular transitive graphs
Pengfei Tang
Considering the wired uniform spanning forest on a nonunimodular transitive graph, we show that almost surely each tree of the wired uniform spanning forest is light. More generall…
A reverse Aldous/Broder algorithm
Yiping Hu, Russell Lyons, Pengfei Tang
The Aldous--Broder algorithm provides a way of sampling a uniformly random spanning tree for finite connected graphs using simple random walk. Namely, start a simple random walk on…
Heavy Bernoulli-percolation clusters are indistinguishable
Pengfei Tang
We prove that the heavy clusters are indistinguishable for Bernoulli percolation on quasi-transitive nonunimodular graphs. As an application, we show that the uniqueness threshold…
Superlinearity of geodesic length in 2 critical first-passage percolation
Michael Damron, Pengfei Tang
First-passage percolation is the study of the metric space , where is a random metric defined as the weighted graph metric using random edge-weights $(t_e)_{e…