Convergence of Discrete Snakes

Svante Janson () and Jean-François Marckert
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Svante Janson: Uppsala University
Jean-François Marckert: Université de Versailles Saint-Quentin

Journal of Theoretical Probability, 2005, vol. 18, issue 3, 615-645

Abstract: Abstract The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if $$\mathbb{E}Y= 0$$ and $$\mathbb{P}(| Y| > y)= o(y^{-4})$$ , then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis $$\mathbb{E}Y^{8+\varepsilon}

Keywords: Brownian snake; discrete snake; limit theorem; weak convergence; ISE; branching random walk (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-005-7252-9

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