Correction to: Optimal Estimate of the Spectral Gap for the Degenerate Goldstein-Taylor Model
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Correction to: Optimal Estimate of the Spectral Gap for the Degenerate Goldstein-Taylor Model Étienne Bernard1 · Francesco Salvarani2,3 Published online: 14 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Correction to: J Stat Phys (2013) 153:363–375 https://doi.org/10.1007/s10955-013-0825-6 In [1], on p. 366, line 5 and on p. 369, line 12, replace “α = 2σ L 1 (T) .” with “σ = 2 min{σ L 1 (T) , −D(0)}, where D(0) is defined in [10], p. 4.”. We underline that the strategy of proof described in [1] is independent of the value of α. The precise formulation of D(0) is recalled below. Let 0 1 Aσ = ∂x x −2σ with
D(Aσ ) = H01 ∩ H 2 ⊕ H01 ,
and denote with sp(Aσ ) the spectrum of Aσ . For R > 0, consider D(R) = sup{Re(λ j ), λ j ∈ sp(Aσ ), |λ j | ≥ R}. The value of D(0) is then obtained in the limit D(0) = lim R→0+ D(R).
The original article can be found online at https://doi.org/10.1007/s10955-013-0825-6.
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Francesco Salvarani [email protected] Étienne Bernard [email protected]
1
Cermics, École des Ponts ParisTech, 6-8 avenue Blaise Pascal, Champs sur Marne, 77455 Marne-la-Vallée Cedex 2, France
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Léonard de Vinci Pôle Universitaire, Research Center, 92916 Paris La Défense, France
3
Dipartimento di Matematica “F. Casorati”, Università degli Studi di Pavia, Via Ferrata 5, 27100 Pavia, Italy
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Spectral Gap for the Degenerate Goldstein-Taylor Model
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Acknowledgements The authors are grateful to the colleagues Anton Arnold and Josephine Evans for pointing out this imprecision.
Reference 1. Bernard, É., Salvarani, F.: Optimal estimate of the spectral gap for the degenerate Goldstein-Taylor model. J. Stat. Phys. 153(2), 363–375 (2013) Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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