The Longtime Behavior of Branching Random Walk in a Catalytic Medium
TLDR
In this article, the branching rate of a particle is given by a random medium fluctuating both in space and time, and it is shown that the time-space random medium (called catalyst) is also a critical branching random walk evolving autonomously while the local branching rate is proportional to the number of catalytic particles present at a site.Abstract:
Consider a countable collection of particles located on a countable group, performing a critical branching random walk where the branching rate of a particle is given by a random medium fluctuating both in space and time. Here we study the case where the time-space random medium (called catalyst) is also a critical branching random walk evolving autonomously while the local branching rate of the reactant process is proportional to the number of catalytic particles present at a site. The catalyst process and the reactant process typically have different underlying motions.read more
Citations
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The shape of large Galton-Watson trees with possibly infinite variance
Jochen Geiger,Lars Kauffmann +1 more
TL;DR: It is shown that random trees whose conditional distribution given their size is the same as the respective conditional distribution of T are Galton-Watson trees conditioned on their total number of leaves.
Journal ArticleDOI
Smooth density field of catalytic super-Brownian motion
Klaus Fleischmann,Achim Klenke +1 more
TL;DR: In this article, a super-Brownian motion (SBM) with local branching rates is considered, and it is shown that the SBM is continuous with a density function, such that the heat equation is solved off the closed support of the time-space measure.
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Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks
TL;DR: In this paper, the scaling limit for a catalytic branching particle system whose particles perform random walks on ℤ and can branch at 0 only is studied, and it is shown that the system converges to a deterministic limit.
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Individuals at the origin in the critical catalytic branching random walk
TL;DR: A conditional limit theorem for the number of individuals at the origin is proved for a continuous time branching random walk on the lattice Z.
Journal ArticleDOI
Interacting Fisher-Wright Diffusions in a Catalytic Medium
TL;DR: In this article, the lifetime behavior of interacting systems in a randomly fluctuating (space-time) medium and focus on models from population genetics was studied, where the local resampling rate (or genetic drift) is proportional to a catalytic medium.
References
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Book
Interacting Particle Systems
TL;DR: The construction, and other general results are given in this paper, with values in [0, ] s. The voter model, the contact process, the nearest-particle system, and the exclusion process.
Journal ArticleDOI
Distribution Function Inequalities for Martingales
TL;DR: In this article, a guide to some recent work in the theory of martingale inequalities is given, and a number of new results are also included; some new proofs are given.
Journal ArticleDOI
Bounds on the Moments of Martingales
TL;DR: In this article, the authors showed that the Marcinkiewicz-Zygmund theorem holds (possibly with a different value of $C_
u$) whenever the $X$'s are independent.