Abstract
The paper contains a gap in the justification of the uniform non degeneracy of the measures \({\mu_\varrho}\), \({\varrho\in\mathcal{J}}\), asserted in Proposition 2.8.1; we used a 0-1 law argument which cannot hold in general due to a conditioning problem; we provide an alternative argument. In the terminology of branching processes, this argument yields new sufficient conditions for an additive martingale on a Galton-Watson tree in varying environment to be almost surely positive conditionally on non extinction of the tree.
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Communicated by F. Toninelli
The online version of the original article can be found under doi:10.1007/s00220-014-2087-9.
The online version of the original article can be found at http://dx.doi.org/10.1007/s00220-014-2087-9.
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Attia, N., Barral, J. Erratum to: Hausdorff and Packing Spectra, Large Deviations, and Free Energy for Branching Random Walks in \({\mathbb{R}^d}\) . Commun. Math. Phys. 351, 873–875 (2017). https://doi.org/10.1007/s00220-016-2826-1
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DOI: https://doi.org/10.1007/s00220-016-2826-1