32 citations · 35 across the 11 of their papers we have counts for
13 papers
Recurrence of strong-decay inhomogeneous long-range percolation clusters
Johannes Bäumler, Lukas Lüchtrath, Christian Mönch
We prove recurrence criteria for inhomogeneous long-range percolation in dimensions one and two. In dimension one, recurrence follows from a purely geometric scarcity condition: lo…
Local structure at the maximum and sharp persistence asymptotics of rough fractional Brownian motion
Christian Mönch
We consider a fractional Brownian motion with Hurst index , and its maximiser on . We show that the rescaled process converges…
(Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on , , and ,
Volker Betz, Alexander Drewitz, Andreas Klippel +1
In this article we investigate the (non)-coincidence of critical parameters for various related percolation problems. More precisely, for the random walk loop soup we show that on…
Partial orders and monotonicity of logarithmic depth and height in preferential attachment trees
Christian Mönch
We study preferential attachment trees with general attachment rules. A natural intuition is that rewarding high-degree vertices more strongly should make the tree shallower. We te…
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…
Inhomogeneous long-range percolation in the weak decay regime
Christian Mönch
We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several…
Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension
Peter Gracar, Lukas Lüchtrath, Christian Mönch
We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large we…
Recurrence versus Transience for Weight-Dependent Random Connection Models
Peter Gracar, Markus Heydenreich, Christian Mönch +1
We investigate random graphs on the points of a Poisson process in -dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point…
Self-similar co-ascent processes and Palm calculus
Christian Mönch
We discuss certain renormalised first passage bridges of self-similar processes. These processes generalise the Brownian co-ascent, a term recently introduced by H. Panzo (Séminair…
Conditionally Poissonian random digraphs
Christian Mönch
We define a Poissonian model of directed random graphs which generalises the undirected Poissonian random graph process introduced by Norros and Reittu in Adv. Appl. Probab. 38 (20…
Persistence probabilities and a decorrelation inequality for the Rosenblatt process and Hermite processes
Frank Aurzada, Christian Mönch
We study persistence probabilities of Hermite processes. As a tool, we derive a general decorrelation inequality for the Rosenblatt process, which is reminiscent of Slepian's lemma…
Distances in scale free networks at criticality
Steffen Dereich, Christian Mönch, Peter Mörters
Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value o…
Relations between - and Pointwise Convergence of Families of Functions Indexed by the Unit Interval
Vaios Laschos, Christian Mönch
We construct a variety of mappings of the unit interval into to generalize classical examples of -convergence of sequences of functions with s…