3 papers
math.PR2026
Subcritical annulus crossing in spatial random graphs
Emmanuel Jacob, Benedikt Jahnel, Lukas Lüchtrath
We consider general continuum percolation models obeying sparseness, translation invariance, and spatial decorrelation. In particular, this includes models constructed on general p…
math.PR2025
All spatial random graphs with weak long-range effects have chemical distance comparable to Euclidean distance
Lukas Lüchtrath
This note provides a sufficient condition for linear lower bounds on chemical distances (compared to the Euclidean distance) in general spatial random graphs. The condition is base…
math.CO2025
A very short proof of Sidorenko's inequality for counts of homomorphism between graphs
Lukas Lüchtrath, Christian Mönch
We provide a very elementary proof of a classical extremality result due to Sidorenko (Discrete Math. 131.1-3, 1994), which states that among all connected graphs on vertic…