Related papers: Approximation for extinction probability of the co…
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
We develop a method for approximating the Gr\"obner basis of the ideal of polynomials which vanish at a finite set of points, when the coordinates of the points are known with only limited precision. The method consists of a preprocessing…
We consider a class of multitype Galton-Watson branching processes with a countably infinite type set $\mathcal{X}_d$ whose mean progeny matrices have a block lower Hessenberg form. For these processes, the probability $\boldsymbol{q}(A)$…
Understanding the relationship between a populations probability of extinction and its carrying capacity frames conservation status assessments and guides efforts to understand and mitigate the ongoing biodiversity crisis. Despite this, our…
We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals of Gibbs point processes in increasing observation windows.…
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…
A new, conceptual proof approach for establishing the existence of regenerative space-time points for symmetric, translation invariant, finite-range interaction contact processes on survival is shown. The proof is elementary, complements…
We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…
The Galaxy and the stars in it form a hierarchical system, such that the properties of individual stars are influenced by those of the Galaxy. Here, an approach is described which uses hierarchical Bayesian models to simultaneously and…
In this work we use the technique of the partial differential approximants to determine, from a pertubative supercritical series expansion for the ulimate survival probability, the critical line of the contact process model in one dimension…
We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…
Recent progress in the study of the contact process [2] has verified that the extinction-survival threshold $\lambda_1$ on a Galton-Watson tree is strictly positive if and only if the offspring distribution $\xi$ has an exponential tail. In…
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
We show that the contact process on the rank-one inhomogeneous random graphs and Erdos-R{\'e}nyi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a…
We consider Galton-Watson branching processes with countable typeset $\mathcal{X}$. We study the vectors ${\bf q}(A)=(q_x(A))_{x\in\mathcal{X}}$ recording the conditional probabilities of extinction in subsets of types $A\subseteq…
We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach in Hofer-Temmel (2019) and Hofer-Temmel and Houdebert (2019) we will use this to couple two…
We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
We present algorithms for computing the reduced Gr\"{o}bner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal.…
Given a branching random walk on a set $X$, we study its extinction probability vectors $\mathbf q(\cdot,A)$. Their components are the probability that the process goes extinct in a fixed $A\subseteq X$, when starting from a vertex $x\in…