Related papers: Shape Theorem for the Contact Process in a Dynamic…
In these lecture notes I present a short review of nuclear shapes, shape coexistence and shape-phase transitions in the interacting boson model. In a study with random interactions it is shown that the appearance of regular spectral…
We study the asymptotic behaviour of occupation times of a transient random walk in quenched random environment on a strip in a sub-diffusive regime. The asymptotic behaviour of hitting times, which is a more traditional object of study, is…
A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…
We study attracting graphs of step skew products from the topological and ergodic points of view where the usual contracting-like assumptions of the fiber dynamics are replaced by weaker merely topological conditions. In this context, we…
This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is…
We analyze the contact Hele-Shaw problem with zero surface tension of a free boundary in a thin domain $\Omega^{\varepsilon}(t).$ Under suitable conditions on the given data, the one-valued local classical solvability of the problem for…
In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove…
The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize…
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…
Deep generative models have demonstrated great performance in image synthesis. However, results deteriorate in case of spatial deformations, since they generate images of objects directly, rather than modeling the intricate interplay of…
We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Shape from texture refers to the extraction of 3D information from 2D images with irregular texture. This paper introduces a statistical framework to learn shape from texture where convex texture elements in a 2D image are represented…
We study local (the heat equation) and nonlocal (convolution type problems with an integrable kernel) evolution problems on a metric connected finite graph in which some of the edges have infinity length. We show that the asymptotic…
We suggest a rigorous definition of the pathwise flux across the boundary of a bounded open set for transient finite energy diffusion processes. The expectation of such a flux has the property of depending only on the current velocity $v$,…
The asymptotic form of the energy density for a gas of particles surrounding a sphere of mass $M$ and radius $R$ is studied using Einstein's equations. It is shown that if the pressure of the gas $p$ varies linearly with the energy density…
It is a fundamental question in epidemiology to estimate, model and predict the growth rate of a pandemic. Analogously, analysing the diffusion of innovation, (fake) news, memes, and rumours is of key importance in the social sciences. The…
The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and…