1 citations · 2 across the 12 of their papers we have counts for
15 papers · 1 filter
Infinite-mean Galton-Watson trees have zero random-interchange threshold
Andreas Klippel, Benjamin Lees, Christian Mönch
We prove that, on a Galton-Watson tree with almost surely finite offspring and infinite offspring mean, the random interchange process has critical parameter zero for infinite cycl…
Critical-curve regularity for finite-lifespan frog models via local-to-global comparisons
Christian Mönch, Andreas Klippel
We study the phase boundary of the finite-lifespan frog model. For rate-one continuous-time simple random walk on an infinite, connected, locally finite transitive graph of superli…
The one-point Schreier Poisson boundary of Thompson's group
Christian Mönch
We identify the Poisson boundary of the one-point Schreier-chain random walk obtained by projecting the simple symmetric random walk on Thompson's group to the dyadic orbit poi…
Age-dependent random connection models with arc reciprocity: clustering and connectivity
Lukas Lüchtrath, Christian Mönch
We introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{re…
Extremes of the zero-average Gaussian Free Field on random regular graphs
Lisa Hartung, Andreas Klippel, Christian Mönch
We study the extreme value statistics of the zero-average Gaussian free field (GFF) on random -regular graphs and the Gaussian free field on -regular trees. For random -re…
Strict monotonicity of critical points in independent long-range percolation models
Stein Andreas Bethuelsen, Christian Mönch
We consider independent long-range percolation models on locally finite vertex-transitive graphs. Using coupling ideas we prove strict monotonicity of the critical points with resp…
Phase transitions for contact processes on sparse random graphs via metastability and local limits
Benedikt Jahnel, Lukas Lüchtrath, Christian Mönch
We propose a new perspective on the asymptotic regimes of fast and slow extinction in the contact process on locally converging sequences of sparse finite graphs. We characterise t…
Loop vs. Bernoulli percolation on trees: strict inequality of critical values
Andreas Klippel, Benjamin Lees, Christian Mönch
We study loop ensembles on locally finite rooted trees. The loops are induced by a Poisson process of links on the edges; the transposition-only case is the random interchange proc…
Phase transitions for contact processes on one-dimensional networks
Benedikt Jahnel, Lukas Lüchtrath, Christian Mönch
We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the…
Inhomogeneous long-range percolation in the strong decay regime: recurrence in one dimension
Christian Mönch
We provide a sufficient criterion for the recurrence of spatial random graphs on the real line based on the scarceness of long-edges. In particular, this complements earlier recurr…
The mean field stubborn voter model
Lisa Hartung, Christian Mönch
We analyse the effect of agent-dependent heavy-tailed waiting times in the voter model on the complete graph with vertices. We derive a novel scaling limit and show the existen…
The number of particles in activated random walk on the complete graph
Antal A. Járai, Christian Mönch, Lorenzo Taggi
We consider an elementary model for self-organised criticality, the activated random walk on the complete graph. We introduce a discrete time Markov chain as follows. At each time…
DAG-type Distributed Ledgers via Young-age Preferential Attachment
Christian Mönch, Amr Rizk
Distributed Ledger Technologies provide a mechanism to achieve ordering among transactions that are scattered on multiple participants with no prerequisite trust relations. This me…
Universality for persistence exponents of local times of self-similar processes with stationary increments
Christian Mönch
We show that , where is the local time measure at of any recurrent -self-similar real-valued process with…
Distances and large deviations in the spatial preferential attachment model
Christian Hirsch, Christian Mönch
We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. Mörters (2013). First, in a regime of strong linear reinforcement,…