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math.PR2025
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…
math.PR2025
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…
math.PR2024
A novel approach to hydrodynamics for long-range generalized exclusion
PatrÃcia 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…