The scaling limit of the interface of the continuous-space symbiotic branching model

@article{Blath2013TheSL,
  title={The scaling limit of the interface of the continuous-space symbiotic branching model},
  author={Jochen Blath and Matthias Hammer and Marcel Ortgiese},
  journal={arXiv: Probability},
  year={2013}
}
The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions, the interface where both populations coexist remains compact. Together with a diffusive scaling property, this suggests the presence of an interesting scaling limit. Indeed, in the present paper, we show weak convergence of the diffusively rescaled populations… 
The symbiotic branching model: Duality and interfaces
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with
The innite rate symbiotic branching model: from discrete to continuous space
The symbiotic branching model describes a spatial population consisting of two types that are allowed to migrate in space and branch locally only if both types are present. We continue our
A new look at duality for the symbiotic branching model
The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlying
Infinite rate symbiotic branching on the real line: The tired frogs model
  • A. Klenke, L. Mytnik
  • Mathematics
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
  • 2020
Consider a population of infinitesimally small frogs on the real line. Initially the frogs on the positive half-line are dormant while those on the negative half-line are awake and move according to
Ancestral lineages in spatial population models with local regulation
TLDR
It is explained how an ancestral lineage can be interpreted as a random walk in a dynamic random environment and defined regeneration times allows to prove central limit theorems for such walks.
The compact interface property for the stochastic heat equation with seed bank
  • F. Nie
  • Mathematics
    Electronic Communications in Probability
  • 2022
We investigate the compact interface property in a recently introduced variant of the stochastic heat equation that incorporates dormancy, or equivalently seed banks. There individuals can enter a

References

SHOWING 1-10 OF 310 REFERENCES
Mutually Catalytic Branching in The Plane: Infinite Measure States
A two-type infinite-measure-valued population in $R^2$ is constructed which undergoes diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the
The Kardar-Parisi-Zhang Equation and Universality Class
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or
Longtime Behavior for Mutually Catalytic Branching with Negative Correlations
In several examples, dualities for interacting diffusion and particle systems permit the study of the longtime behavior of solutions. A particularly difficult model in which many techniques collapse
The asymptotic behavior of fragmentation processes
The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the evolution of a mass that falls apart randomly as time passes. We investigate
Nonintersecting Brownian Motions on the Half-Line and Discrete Gaussian Orthogonal Polynomials
We study the distribution of the maximal height of the outermost path in the model of N nonintersecting Brownian motions on the half-line as N→∞, showing that it converges in the proper scaling to
Critical behavior of nonintersecting Brownian motions at a tacnode
We study a model of n one‐dimensional, nonintersecting Brownian motions with two prescribed starting points at time t = 0 and two prescribed ending points at time t = 1 in a critical regime where the
Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions
We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be
...
...