We analyze multilayer neural networks in the asymptotic regime of simultaneously (a) large
network sizes and (b) large numbers of stochastic gradient descent training iterations. We …

These notes provide a review of basic stochastic population models including branching
processes and models of population genetics. Measure-valued population models including …

We consider particle systems in locally compact Abelian groups with particles moving
according to a process with symmetric stationary independent increments and undergoing …

A class of measure-valued processes which model multilevel multitype populations
undergoing mutation, selection, genetic drift and spatial migration is considered. We …

We consider a stochastic individual-based population model with competition, trait-structure
affecting reproduction and survival, and changing environment. The changes of traits are …

The notion of degree and related notions concerning recurrence and transience for a class
of Lévy processes on metric Abelian groups are studied. The case of random walks on a …

This is a survey of recent work on hierarchical random walks with emphasis on transience-
recurrence phenomena and in particular on the notion of order of transience. A family of …

With the algebraic trees, L\" ohr and Winter (2021) introduced a generalization of the notion
of graph-theoretic trees to account for potentially uncountable structures. The tree structure …

This paper considers the following generalized almost sure local extinction for the d-
dimensional (1+ β)-super-Brownian motion X starting from Lebesgue measure on Rd. For …

The high-density asymptotic behaviour of a two-level branching system in Rd is studied. In
the finite-variance case, a fluctuation limit process is obtained which is characterized as a …