Spatial continuum limit of tree-valued state-dependent spatial branching processes

点击翻译按钮获取中文摘要

The project studies the spatial continuum limit of one- and multitype branching processes with state-dependent branching rates and analyses the characteristics of limit processes. Particular emphasis is placed on genealogies in the corresponding populations, i.e. tree-valued processes are studied. Typical examples are branching random walks, catalytic branching random walks, mutually branching random walks, self-catalytic random walks and logistic branching random walks and the relevant continuous mass limits (interacting branching diffusions). The goal is to show the existence of the limits, the characteristics of their longtime behaviour and the structure on small space and time scales. The question of their stochasticity shall be clarified and in the case of a deterministic limit the asymptotic of ''hotspots'' shall be studied by means of volatility or size biasing and subsequent rescaling. As basis the calculus of infinitely divisible genealogical processes and the description of genealogies of matri- and patrilinear ancestor lines are to be developed.