5 papers
Computer-aided solution to the -bonacci pick-up sticks problem
Julian Kern
A full solution to the recently proposed problem of determining the probability that no -gon can be built from independently and uniformly chosen sticks in is propos…
Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities
Marta Dai Pra, Julian Kern
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective ad…
A novel approach to hydrodynamics for long-range generalized exclusion
Patrícia Gonçalves, Julian Kern, Lu Xu
We consider a class of generalized long-range exclusion processes evolving either on or on a finite lattice with an open boundary. The jump rates are given in terms of…
A -Fleming-Viot type model with intrinsically varying population size
Julian Kern, Bastian Wiederhold
We propose an extension of the classical -Fleming-Viot model to intrinsically varying population sizes. During events, instead of replacing a proportion of the population, a ran…
Weak reservoirs are superexponentially irrelevant for misanthrope processes
Julian Kern
We provide a short proof for the exponential equivalence between misanthrope processes in contact with weak reservoirs and those with impermeable boundaries. As a consequence, we c…