49 citations · 157 across the 34 of their papers we have counts for
36 papers · 1 filter
Markov processes forced on a subspace by a large drift, with applications to population genetics
Samuel Ayomide Adeosun, Peter Pfaffelhuber
Consider a sequence of Markov processes with state space , where has a strong drift to , such that is slow for some appropriate $Φ:…
A diploid population model for copy number variation of genetic elements
Peter Pfaffelhuber, Anton Wakolbinger
We study the following model for a diploid population of constant size : Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the tw…
A unified framework for limit results in Chemical Reaction Networks on multiple time-scales
Timo Enger, Peter Pfaffelhuber
If is a sequence of Markov processes which solve the martingale problems for some operators , it is a classical task to derive a limit result…
The Martingale Problem Method Revisited
David Criens, Peter Pfaffelhuber, Thorsten Schmidt
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is n…
Mean-field limits for non-linear Hawkes processes with excitation and inhibition
Peter Pfaffelhuber, Stefan Rotter, Jakob Stiefel
We study a multivariate, non-linear Hawkes process on the complete graph with nodes. Each vertex is either excitatory (probability ) or inhibitory (probability ).…
Modifiers of mutation rate in selectively fluctuating environments
Franz Baumdicker, Elisabeth Huss, Peter Pfaffelhuber
We study a mutation-selection model with a fluctuating environment. More precisely, individuals in a large population are assumed to have a modifier locus determining the mutation…
Duality and the well-posedness of a martingale problem
Andrej Depperschmidt, Andreas Greven, Peter Pfaffelhuber
For two Polish state spaces and , and an operator , we obtain existence and uniqueness of a -martingale problem provided there is a bounded continuous duality…
The partial duplication random graph with edge deletion
Felix Hermann, Peter Pfaffelhuber
We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex…
The range of once-reinforced random walk in one dimension
Peter Pfaffelhuber, Jakob Stiefel
We study once-reinforced random walk (ORRW) on . For this model, we derive limit results on all moments of its range using Tauberian theory.
Markov branching processes with disasters: extinction, survival and duality to p-jump processes
F. Hermann, P. Pfaffelhuber
A -jump process is a piecewise deterministic Markov process with jumps by a factor of . We prove a limit theorem for such processes on the unit interval. Via duality with res…
The independent loss model with ordered insertions for the evolution of CRISPR spacers
Franz Baumdicker, Ariana M. I. Huebner, Peter Pfaffelhuber
Today, the CRISPR (clustered regularly interspaced short palindromic repeats) region within bacterial and archaeal genomes is known to encode an adaptive immune system. We rely on…
The fixation probability and time for a doubly beneficial mutant
Sebastian Bossert, Peter Pfaffelhuber
For a highly beneficial mutant entering a randomly reproducing population of constant size, we study the situation when a second beneficial mutant arises before has fix…
A spatial model for selection and cooperation
Peter Czuppon, Peter Pfaffelhuber
We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called…
A mixing tree-valued process arising under neutral evolution with recombination
Andrej Depperschmidt, Etienne Pardoux, Peter Pfaffelhuber
The genealogy at a single locus of a constant size population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination…
Stochastic averaging for multiscale Markov processes with an application to a Wright-Fisher model with fluctuating selection
Martin Hutzenthaler, Peter Pfaffelhuber, Clemens Printz
Let be an ergodic Markov process and, for every , let drive a process . Classical results sho…
Large-scale behavior of the partial duplication random graph
Felix Hermann, Peter Pfaffelhuber
The following random graph model was introduced for the evolution of protein-protein interaction networks: Let be a sequence of random graph…
Some limit results for Markov chains indexed by trees
Peter Czuppon, Peter Pfaffelhuber
We consider a sequence of Markov chains with , indexed by the full binary tree $\mathcal T = \mathcal T_0 \cup…
The fixation time of a strongly beneficial allele in a structured population
Andreas Greven, Peter Pfaffelhuber, Cornelia Pokalyuk +1
For a beneficial allele which enters a large unstructured population and eventually goes to fixation, it is known that the time to fixation is approximately for a larg…
The stationary distribution of a Markov jump process glued together from two state spaces at two vertices
Bence Mélykúti, Peter Pfaffelhuber
We compute the stationary distribution of a continuous-time Markov chain which is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of stat…
Some large deviations in Kingman's coalescent
Andrej Depperschmidt, Peter Pfaffelhuber, Annika Scheuringer
Kingman's coalescent is a random tree that arises from classical population genetic models such as the Moran model. The individuals alive in these models correspond to the leaves i…
Scaling limits of spatial compartment models for chemical reaction networks
Peter Pfaffelhuber, Lea Popovic
We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The…
The infinitely many genes model with horizontal gene transfer
Franz Baumdicker, Peter Pfaffelhuber
The genome of bacterial species is much more flexible than that of eukaryotes. Moreover, the distributed genome hypothesis for bacteria states that the total number of genes presen…
Path-properties of the tree-valued Fleming-Viot process
Andrej Depperschmidt, Andreas Greven, Peter Pfaffelhuber
We consider the tree-valued Fleming-Viot process, , with mutation and selection as studied in Depperschmidt, Greven, Pfaffelhuber (2012). This process mod…
Realistic extensions of a Brownian ratchet for protein translocation
A. Depperschmidt, N. Ketterer, P. Pfaffelhuber
We study a model for the translocation of proteins across membranes through a nanopore using a ratcheting mechanism. When the protein enters the nanopore it diffuses in and out of…