Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

Achim Klenke; Leonid Mytnik

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Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

Achim Klenke, Leonid Mytnik

Probability · Submitted 21 Oct 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent.

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arXiv ID0910.4120 (version 2)

Pith IDEYYIKOL6, Pith's permanent record of this paper and its review

CitationAchim Klenke, Leonid Mytnik. "Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior." arXiv:0910.4120 (2009). https://pith.science/paper/EYYIKOL6

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.35 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.20 · mentions code or data availability 0.02.

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Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies.	background 0.78	0.14	0.02	unclear 0.88
s1	Construction, characterization and convergence (2008) Preprint] and [Ann.	background 0.99	0.05	0.02	unclear 0.99
s2	Probab. 38 (2010) 479-497].	background 0.99	0.04	0.02	unclear 0.99
s3	For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent.	result 1.00	0.93	0.48	asserted 1.00
s4	On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.	result 1.00	0.93	0.26	asserted 0.93

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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Original abstract

Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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We could proceed in two ways to construct $X^K$: * We could imitate the SPDE construction of $X$ (see [ref] ) by replacing the intensity measure on $E$ of the Poisson point process by a suitable intensity measure on $[0,K]^2∖(0,K)^2$. * We could imitate the Trotter type construction of $X$ (see [ref] ) by replacing the harmonic measure $Q$ on $[0,∞)^2$ by the harmonic measure $Q^K$ on $[0,K]^2$.

Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence · Construction of the Truncated Process · 0.97

Cites as background 2 papers

In [ref] the IMUB process $X$ was constructed for countable $S$ via approximate solutions to a related Poisson noise stochastic partial differential equation.

Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence · Background and Motivation · 0.89
In [ref] the infinite rate mutually catalytic branching process $X$ was constructed for $S$ a singleton.

Infinite rate mutually catalytic branching · Background and Motivation · 0.90

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