7 papers
Fixed forests in the minimum spanning tree and cubic volume growth
Luca Makowiec
Let be the minimum spanning tree of the complete graph with i.i.d.\ uniform edge weights. For a fixed forest with connected components , we show t…
Critical curve of loop percolation on the -regular tree
Luca Makowiec, Artem Sapozhnikov
We consider clusters formed by a Poisson ensemble of random walk loops on the -regular tree with an intensity parameter and a killing parameter ; the latter penali…
Local limits of random spanning trees in random environment
Luca Makowiec
We study the edge overlap and local limit of the random spanning tree in random environment (RSTRE) on the complete graph with vertices and weights given by for…
Random spanning trees in random environment
Luca Makowiec, Michele Salvi, Rongfeng Sun
We introduce a new spanning tree model called the random spanning tree in random environment (RSTRE), which interpolates between the uniform spanning tree and the minimum spanning…
Repeat times and a two-weight UST model
Umberto De Ambroggio, Luca Makowiec
We study a model of random weighted uniform spanning trees on the complete graph with vertices, where each edge is assigned a weight of with probability and $1…
Observables of random spanning trees in random environment
Luca Makowiec
In this thesis, we study a new disordered system called random spanning tree in random environment (RSTRE) across different families of graphs with varying disorder distributions.…