Limiting laws of supercritical branching random walks

DOI10.1016/j.crma.2012.05.013zbMath1260.60173arXiv1203.5445OpenAlexW2134395001MaRDI QIDQ432692

Julien Barral, Rémi Rhodes, Vincent Vargas

Publication date: 4 July 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.5445

zbMATH Keywords

convergence in lawGalton-Watson treebranching random walklimit lawmeasure change

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (20)

The near-critical Gibbs measure of the branching random walk ⋮ Glassy phase and freezing of log-correlated Gaussian potentials ⋮ Gaussian multiplicative chaos and KPZ duality ⋮ The endpoint distribution of directed polymers ⋮ Critical Mandelbrot cascades ⋮ Basic properties of critical lognormal multiplicative chaos ⋮ Hausdorff and packing spectra, large deviations, and free energy for branching random walks in \({\mathbb{R}^d}\) ⋮ Towards rigorous analysis of the Levitov–Mirlin–Evers recursion ⋮ Maximum of a log-correlated Gaussian field ⋮ Localization in Gaussian disordered systems at low temperature ⋮ Critical Gaussian multiplicative chaos: convergence of the derivative martingale ⋮ Gaussian multiplicative chaos and applications: a review ⋮ On exact scaling log-infinitely divisible cascades ⋮ Localization of directed polymers with general reference walk ⋮ Extremes of local times for simple random walks on symmetric trees ⋮ The glassy phase of complex branching Brownian motion ⋮ Genealogy of the extremal process of the branching random walk ⋮ Fluctuation lower bounds in planar random growth models ⋮ Decompositions of log-correlated fields with applications ⋮ Local fluctuations of critical Mandelbrot cascades

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• Fixed points of a generalized smoothing transformation and applications to the branching random walk
• Fixed points of the smoothing transformation
• Measure change in multitype branching
• Continuity of the multifractal spectrum of a random statistically self-similar measure

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