We study independent long-range percolation on Z d for all dimensions d, where the vertices
u and v are connected with probability 1 for‖ uv‖∞= 1 and with probability p (β,{u, v})= 1-e …

Behavior of the distance exponent for |x−y|2d long-range percolation Page 1 Behavior of the
distance exponent for 1 |x−y|2d long-range percolation Johannes Bäumler∗ August 9, 2022 …

The study of first passage percolation (FPP) for the random interlacements model has been
initiated in arXiv: 2112.12096, where it is shown that on $\mathbb {Z}^ d $, $ d\geq 3$, the …

We study independent long-range percolation on $\mathbb {Z}^ d $ where the vertices $ u $
and $ v $ are connected with probability 1 for $\| uv\| _\infty= 1$ and with probability $1-e …

In this thesis, we study long-range percolation at critical phases. We consider the graph
distances for the long-range percolation graph with critical decay parameter and we provide …

We study the growth and isoperimetry of infinite clusters in slightly supercritical Bernoulli
bond percolation on transitive nonamenable graphs under the L 2 boundedness condition …